The All-Star right-hander was scheduled to start Friday night in New York, but he returned Thursday morning to Los Angeles, where wife Emily delivered their first child, son Bode Nicholas.
The Dodgers recalled right-hander Josh Ravin from Triple-A Oklahoma City to fill Greinke's roster spot. Left-handed reliever Ian Thomas was set to start Friday night.
Greinke can remain on the paternity list for up to three days, but manager Don Mattingly said he hopes Greinke will return in time to start against the Mets on Saturday or Sunday.
Greinke (9-2) leads the majors with a 1.30 ERA and has not allowed a run in 43 2/3 innings. The major-league record is 59, set by Dodgers ace Orel Hershiser in 1988.