Peet went into labor Wednesday instead of keeping plans to attend a Hollywood luncheon, the Post's Page Six reported, citing an unnamed friend of the star.
The source told the Post that Peet was rushed to a nearby hospital. Peet's representative confirmed the birth of the baby, but wouldn't give any other details.
Peet and Benioff married in September after a four-year relationship.
Since the fall, Peet has starred in the NBC dramedy "Studio 60 on the Sunset Strip," which takes place behind the scenes of a "Saturday Night Live" comedy sketch show and was created by "West Wing" mastermind Aaron Sorkin. Rumors of an imminent cancellation have dogged the show almost since its September premiere.
Peet also had roles in films including "Syriana," "Something's Gotta Give" and "The Whole Nine Yards."