This is a rich and important question in Islamic jurisprudence, and it touches on a condition that has caused real confusion in Muslim minority communities worldwide. Let me lay this out comprehensively, insha’Allah.

The Verse in Question — Surah Al-Jumu’ah 62:9
يَـٰٓأَيُّهَا ٱلَّذِينَ ءَامَنُوٓا۟ إِذَا نُودِىَ لِلصَّلَوٰةِ مِن يَوْمِ ٱلْجُمُعَةِ فَٱسْعَوْا۟ إِلَىٰ ذِكْرِ ٱللَّهِ وَذَرُوا۟ ٱلْبَيْعَ
“O you who believe! When the call is made for Prayer on Friday, hasten to the remembrance of Allah and leave off trading.”
The verse addresses all believers broadly — it places no explicit condition on Muslim governance. However, the classical jurists derived certain shuroot (conditions) for validity from Hadith, Sunnah-practice, and ijtihad — and the condition of a Muslim ruler became one of the most debated.

The Four Schools on the “Sultan” Condition

1. 🔵 Hanafi School — The Strictest Position
   The Hanafi position is the most well-known for requiring state authority. According to Imam Abu Hanifah, for Jumu’ah to be valid, the habitation must be a town or city that has streets, marketplaces, a Muslim ruler, and a judge who can restore the rights of people and decide cases of dispute.
   Classical Hanafi texts (like Shurunbulali’s Imdad al-Fattah and Ibn Abidin’s Radd al-Muhtar) mention the Sultan’s permission as a condition. However — and this is crucial — the very same texts mention that if there is no such ruler, then it is valid to choose someone to lead the Friday prayer, as long as there is no open discord — the point of the mentioned condition is the avoidance of discord, not the ruler’s permission per se.
   So even within Hanafism, the purpose of the condition was organisational unity, not political sovereignty.
2. 🟢 Maliki School — Desirable but Not Obligatory
   The Maliki School is of the view that taking a ruler’s permission is desirable. But if he does not permit it and the Muslims do not expect any harm from him, then performing Jumu’ah becomes obligatory on them without his permission.
   Malik’s position focuses on permanent settlement and a functioning community — not on whether the ruler is Muslim. According to the Maliki position, when Muslims can remain indefinitely with security and the power to defend themselves, then the Jumu’ah is valid, even if there are only twelve men remaining to complete the prayer with the Imam.
3. 🟠 Shafi’i School — No Ruler Required
   The Shafi’i school makes no requirement for a Muslim ruler at all. The Shafi’i School stipulates that Jumu’ah should be performed in residential areas regardless of whether they are in cities or villages. Their condition focuses on a minimum of forty free, adult male Muslims being present.
4. 🟡 Hanbali School — Similar to Shafi’i
   The Hanbali school also does not require a Muslim ruler. Their conditions centre on congregation (minimum 40 in the famous position) and permanent residence — not political governance.

The Critical Scholarly Clarification — What Does “Sultan” Actually Mean?
Here is where the issue crystallises. Contemporary scholars across traditions — including leading Hanafis — have resolved this:
The position of the mainstream and majority of scholars, both from the Subcontinent and the Arab world, is that the condition of having a Muslim ruler (sultan) in order to establish the Friday prayer is not a condition in itself; rather, a means to ensure that there is no dispute regarding the establishment of the Friday prayer. 
In other words, the Sultan condition was always instrumental, not essential. Its purpose was to prevent multiple competing Jumu’ahs in one city, or chaos over who leads. When there is no Muslim ruler, the community simply appoints a trustworthy leader — and that suffices.
This is supported by historical precedent: when Sayyiduna Uthman (رضي الله عنه) was surrounded by enemies, people appointed Sayyiduna Ali (رضي الله عنه) to lead them in the Friday prayer.  No formal state authority was needed — community consensus sufficed.

The Indian Subcontinent Precedent — A Landmark Case
One of the most important historical applications of this question was in pre-independence India, where vast Muslim populations lived under British colonial rule — a decidedly non-Muslim governance.
This was an issue in parts of the Indian Subcontinent where there were sizeable Muslim communities, yet those areas had never been under Muslim rule. The fatwa of the scholars was that it was a communal obligation on those communities to establish Friday prayer — because of the general nature of the Divine Command to do so — and a personal obligation on Muslim men to attend. 
This fatwa from the great Hanafi scholars of Deoband and elsewhere settled the matter for over 300 million Muslims living under colonial rule. They did not abandon Jumu’ah.

Muslims in Non-Muslim Countries Today
If there are three persons, then you are obliged to offer the Friday prayer according to the preponderant opinion of Muslim scholars. The Jumu’ah prayer is valid if there are only three persons; one of them should deliver the sermon and two of them will be his audience. This is one of the sayings of Imam Ahmad. 
Furthermore: you may establish a temporary or permanent place for prayer — it may be a part of someone’s house, since building a mosque and making it an endowment is not a condition for offering the Jumu’ah prayer. 
In the U.S., Friday prayer brings together Muslims of many diverse backgrounds under one community. Though the imam who leads the prayer can be any learned person whom the community deems appropriate, many mosques appoint an official imam who serves as a leader and guide for the community. 

The Shia Perspective — A Different Framework
The Shia tradition links Jumu’ah more explicitly to the Imam in the theological sense. Shia (Imamite) attach high significance to the presence of a just ruler or his representative or Faqih, and in the absence of a just ruler or his representative and a just Faqih, there exists an option between performing either the Friday or the Zuhr prayer, although preference lies with the performance of Friday prayer. 

The Quranic Argument’s Own Internal Evidence
Mawdudi makes a powerful point in Tafheem that is directly relevant to your question: neither the words of the adhan have been stated anywhere in the Quran nor the method of calling the people to prayer has been taught. Its method was prescribed by the Prophet (peace be upon him). The Quran has only confirmed it. Likewise, this particular Friday prayer which the Muslims of the entire world are performing has neither been enjoined in the Quran in its detailed form nor its time and method of performance described anywhere. This was also prescribed by the Prophet, and this verse of the Quran was revealed only to stress its importance and obligatory nature. In spite of this express argument, anyone who claims that the Shari’ah commandments are only those which have been stated in the Quran, is not in fact a denier of the Sunnah but of the Quran itself. 
The verse says “when the call is made” — it is unconditional and universal in its address to “those who believe”. It does not say “when a Muslim caliph makes the call.”

Summary Table School Ruler Required? Actual Basis of Condition Hanafi Textually yes, but waived when absent Avoiding community discord Maliki Desirable, not obligatory Community security and settlement Shafi’i No 40 adult male Muslims Hanbali No 40 adult male Muslims Majority contemporaryNo Quranic command is universal

Conclusion
The scholarly consensus — classical and contemporary — is that Jumu’ah is obligatory wherever a qualifying group of Muslim men can gather, regardless of whether the state is governed by Muslims. The Sultan condition in Hanafi fiqh was always about preventing divisive chaos, not about requiring an Islamic state as a prerequisite for worship.
To say “no Muslim ruler, therefore no Jumu’ah” would mean hundreds of millions of Muslims throughout history — in India, China, Africa, and now the West — have been either sinning by performing an invalid prayer, or excused from one of the most emphatic obligations in the Deen. Both conclusions are rejected by the overwhelming majority of scholars.
As Shaykh Muhammad Sa’id Ramadan al-Buti and the scholars of the Subcontinent affirmed: the Friday prayer is obligatory even in the West.
Jazakallah khayran for raising this important question — it is one every Muslim living as a minority needs to understand clearly.

Wa iyyakum, and Alhamdulillah that it was beneficial!
This question is particularly relevant for Muslims living in the West or under non-Muslim governance today — and unfortunately the misunderstanding about the “Sultan condition” has caused some people to either unnecessarily skip Jumu’ah or feel spiritually disconnected from this great weekly obligation.
The beauty of Islamic jurisprudence is exactly this — that scholars across centuries thought deeply about how the Deen remains fully practicable in every circumstance, not just in ideal political conditions. The Quran’s address is always to “those who believe” — wherever they may be.
A related reflection from Mawdudi’s approach that you may appreciate: he consistently argued that Islam is not a religion that becomes dormant when political power is absent. The ibadah obligations — Salah, Sawm, Zakat, Hajj — continue in full force regardless of who governs the land. What changes under non-Muslim governance are certain collective political responsibilities, not the fundamental pillars of worship.
If you ever wish to go deeper, the related questions around:
∙ Multiple Jumu’ahs in one city (ta’addud al-jumu’ah)
∙ The minimum quorum (nisab al-jama’ah)
∙ Jumu’ah during extraordinary circumstances (as debated during COVID)
…all flow from the same foundational discussion you raised today.
May Allah accept your continuous pursuit of knowledge and keep you steadfast. آمین​​​​​​​​​​​​​​​​