No. They go back to the prophet and patriarch Abraham, and their three prophets are directly descended from his sons - Muhammed from the eldest, Ishmael, and Moses and Jesus from Isaac. Abraham established the settlement which today is the city of Makkah, and built the Ka'abah towards which all Muslims turn when they pray.
This diagram shows how the three prophets are directly descended from the two sons of Abraham, Ishmael and Isaac. Muhammad is a descendant of the eldest son, Ishmael. Moses and Jesus descended from Isaac. Abraham established a settlement, which today is the city of Makkah and built the Ka'abah towards which all Muslims turn when they pray.
Furthermore, throughout the Muslim holy book, the Qur'an, the links between these religions are affirmed:
"Say: We believe in God, and in that which has been sent
down on us, and that sent down on Abraham, Ishmael,
Isaac, Jacob, and their descendants, and that which was
given to Moses and Jesus, and was given to all the prophets,
from their Lord; we make no distinction between any of
them; and we surrender ourselves to God alone."
Christians and Jews hold a special place in Islam. They are called the People of the Book (Ahl al-Kitab), since the original Torah and Gospel were also divinely revealed and they shared in the prophetic tradition. True Islamic states have always shown their religious minorities tolerance and respect and those communities flourished under Islamic rule. God says:
"...Those who believe (in the message of Islam), and the
Jews, the Sabaeans, and the Christians - all those who
believe in Allah and the Last Day, and act righteously - no
fear shall come upon them..." (Qur'an 5:69)