The Quran

يا أَيُّهَا الَّذينَ آمَنوا أَطيعُوا اللَّهَ وَأَطيعُوا الرَّسولَ وَأُولِي الأَمرِ مِنكُم ۖ فَإِن تَنازَعتُم في شَيءٍ فَرُدّوهُ إِلَى اللَّهِ وَالرَّسولِ إِن كُنتُم تُؤمِنونَ بِاللَّهِ وَاليَومِ الآخِرِ ۚ ذٰلِكَ خَيرٌ وَأَحسَنُ تَأويلًا

Muhammad Asad

O you who have attained to faith! Pay heed unto God, and pay heed unto the Apostle and unto those from among you¹ who have been entrusted with authority; and if you are at variance over any matter, refer it unto God and the Apostle,² if you [truly] believe in God and the Last Day. This is the best [for you], and best in the end.³

I.e., from among the believers.
I.e., to the Qur'an and to the sunnah (the sayings and the practice) of the Prophet. See also verse 65 of this surah.
Read in conjunction with 3:26, which speaks of God as "the Lord of all dominion" - and therefore the ultimate source of all moral and political authority - the above passage lays down a fundamental rule of conduct for the individual believer as well as the conceptual basis for the conduct of the Islamic state. Political power is held in trust (amanah) from God; and His will, as manifested in the ordinances comprising the Law of Islam, is the real source of all sovereignty. The stress, in this context, on "those from among you who have been entrusted with authority" makes it clear that the holders of authority (ulu l-amr) in an Islamic state must be Muslims.