Meyer, a 29-year-old jewelry designer, gave birth Thursday in Los Angeles, Us Weekly and People magazines reported on their Web sites.
Maguire, 31, and Meyer have been together since 2003. They announced their engagement this year.
Maguire, whose latest "Spider-Man" installment, "Spider-Man 3," is due next year, has also starred in such films as "Seabiscuit" and "Wonder Boys."
Maguire's publicist did not immediately respond to phone messages from The Associated Press.