Who founded the Muslim Church?

Answer 1

There is no such thing as "the Muslim Church", so there are two possible questions that you may have intended by the phrasing of the question:

1) Who founded the religion of Islam?
For many Muslims the term "Islam" has two meanings: the Divine Religion of Submission to God's Will (often called Islam with a small "i") and the Institutionalized Belief as Found in Qur'an and Revealed by Mohammed's Prophecy (often called Islam with a capital "I").

islam with a small "i" is a concept that comes out of Islam with a capital "I" and projects the Established Religion of Islam back into the period before would have identified as Muslim. The purpose of said belief, in a functional sense, is to gird Islam in the history afforded by the Judeo-Christian prophetic lineage and ensure its authenticity. islam also affords the believer in Islam a continuity of tradition which Mohammed only continued and corrected as opposed to having the religion of Islam be an affront or disagreement with other divinely-inspired religions. Since islam is derivative of Islam, it does not actually exist prior to Islam.

Islam, as an Established Religion, was organized and directed by Mohammed, who was born in 570 C.E. at Mecca, in Saudi Arabia. According to Islam, he received revelations from God in Mecca in from the year 610-632 C.E. He was supported by several family members like his uncle Ali Ibn Talib and his first wife Khadija to pursue these prophecies. He converted other members to his nascent religion before being expelled from Mecca to Yethrib (now known as Medina) in 622 C.E. When Mohammed became the Chief Hakam or Judge/Administrator of Yethrib, he received many new revelations and began to ask members of his community to memorize these revelations (along with prior ones). These memorizers (in Arabic Hafeths) would eventually be responsible for the creation of one unified Qur'an. By Mohammed's death, he had conquered all of Arabia and converted most of Arabia to his new faith, establishing the grounds for an Islamic Caliphate, which succeeded him.

2) Who founded the centralized structure of Islam?
Islam does not currently have a centralized structure. Sunni Islam is congregationalist while Shiite and Ibadi Islam are regionally organized (similar to Orthodox Christianity).

However, Islam once had a centralized structure and its form of the Caliphate was founded partially by Muhammad himself in his function as a cleric and a statesman. After his death, the position formalized as an authoritarian religious leader and the position became one recognized only by Sunnis. Non-Sunnis (Shiites, Kharijites, and Ibadis) became more regionally organized. However, the centralized authority of the Caliphate was broken in the 900s C.E. when the expelled Umayyads in Spain proclaimed a Caliphate in addition to the centrally recognized one by the Abbassids. This situation of there being a central Caliph and weaker competitor caliphs continued until the 1930s when Turkish President Ataturk abolished the Caliphate and made Sunni Islam a congregationalist religion.

Answer 2

There is no "Muslim Church". However, the place where Muslims pray is called a mosque.