Although the word "Islam" is not mentioned directly in the Bible, there is recorded an outline of the Arabic people as the Children of Abraham who inhabited the "eastern country". So the history of the Muslim people (people who believe in Islam) begins with the prophet Abraham and his descendants through Ishmael, his firstborn son.
Abraham's first-born son by Hagar the Egyptian was Ishmael. It's in the Bible, the Torah, Genesis 16:15, RSV. "And Hagar bore Abram a son; and Abram called the name of his son, whom Hagar bore, Ishmael. Abram was eighty-six years old when Hagar bore Ishmael to Abram."
Abraham was given a special promise that the descendants of Ishmael would become a great nation. It's in the Bible, the Torah, Genesis 17:20, RSV. "As for Ishmael, I have heard you; behold, I will bless him and make him fruitful and multiply him exceedingly; he shall be the father of twelve princes, and I will make him a great nation."
His name (Ishmael) was given by God and means "God hears." It's in the Bible, the Torah, Genesis 16:10, 11, RSV. "The angel of the Lord also said to her, "I will so greatly multiply your descendants that they cannot be numbered for multitude." And the angel of the Lord said to her, "Behold, you are with child, and shall bear a son; you shall call his name Ishmael; because the Lord has given heed to your affliction."
The descendants of Ishmael and the other sons of Abraham through Keturah were given the eastern country and are referred to as the children or people of the east. They are the forefathers of the Arabs. Muhammad, the prophet of Islam, traces his lineage back to Ishmael through his first born son, Nabaioth. It's in the Bible, the Torah, Genesis 25:6, 12-18, RSV. "But to the sons of his concubines Abraham gave gifts, and while he was still living he sent them away from his son Isaac, eastward to the east country." "These are the descendants of Ishmael, Abraham's son, whom Hagar the Egyptian, Sarah's maid, bore to Abraham. These are the names of the sons of Ishmael, named in the order of their birth: Nebaioth, the first-born of Ishmael; and Kedar, Adbeel, Mibsam, Mishma, Dumah, Massa, Hadad, Tema, Jetur, Naphish, and Kedemah. These are the sons of Ishmael and these are their names, by their villages and by their encampments, twelve princes according to their tribes. (These are the years of the life of Ishmael, a hundred and thirty-seven years; he breathed his last and died, and was gathered to his kindred.) They dwelt from Havilah to Shur, which is opposite Egypt in the direction of Assyria; he settled over against all his people." The areas noted here in verse 18 are located in Central and Northern Arabia.
Wise men, from the east (from Persia), brought gifts to the infant Jesus. It's in the Bible, the Injil, Matthew 2:1, 2, 9-12, RSV. "Now when Jesus was born in Bethlehem of Judea in the days of Herod the king, behold, wise men from the East came to Jerusalem, saying, 'Where is he who has been born king of the Jews? For we have seen his star in the East, and have come to worship him.' … When they had heard the king they went their way; and lo, the star which they had seen in the East went before them, till it came to rest over the place where the child was. When they saw the star, they rejoiced exceedingly with great joy; and going into the house they saw the child with Mary his mother, and they fell down and worshipped him. Then, opening their treasures, they offered him gifts, gold and frankincense, and myrrh. And being warned in a dream not to return to Herod, they departed to their own country by another way."
Descendants of Abraham through Ishmael are predicted to bring their praise into the temple of God. This is interpreted by most scholars to refer to the gathering of the peoples in the New Earth, heaven, paradise. It's in the Bible, the Torah, Isaiah 60:6, 7, RSV. "A multitude of camels shall cover you, the young camels of Midian and Ephah; all those from Sheba shall come. They shall bring gold and frankincense, and shall proclaim the praise of the Lord. All the flocks of Kedar shall be gathered to you, the rams of Nebaioth shall minister to you; they shall come up with acceptance on my alter, and I will glorify my glorious house." These are all sons of Abraham, children of the East, Arabs, forefathers of the Muslim people.
(For additional information on the Biblical history of Muslims, see the Common Questions/ section.)