The 7-pound, 7-ounce baby was born Tuesday in Los Angeles, E! Online reported.
Mother and baby are "doing well," said a statement from their rep.
Suri means "princess" in Hebrew and "red rose" in Persian, the statement said.
Cruise, 43, has been quoted as saying he would marry Holmes, 27, after their baby was born. The couple have been dating for about a year.