Rookie Dirk Hayhurst (0-2, 8.49 ERA) replaced Peavy on Friday for the first game of a three-game series against Washington at Nationals Park.
Peavy called manager Bud Black around 12:30 a.m. on Friday to inform him that his wife was in labor.
"We knew this was a possibility early in the week," Black said. "I think that everyone was holding out hope Katie could hold off a few more days. But nature took its course."
As of Friday afternoon, Katie Peavy hadn't yet given birth. The Peavys already have two boys: Jacob (7) and Wyatt (4).
Peavy (9-11, 2.77 ERA) will rejoin the team on Tuesday in Los Angeles, where he will start against the Dodgers. Black didn't rule out Peavy returning for the last game of the regular season on Sept. 28.
Peavy is the defending National League Cy Young Award winner.
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.