The team then recalled outfielder Alex Dickerson from Triple-A El Paso to take Venable's spot on the roster.
Dickerson, who was with El Paso during a series in Albuquerque, N.M., on Wednesday, was expected to arrive in time for Thursday's 11:10 a.m. PT game at Miller Park.
Dickerson got into Thursday's 10-1 loss to the Brewers in the eighth inning Thursday, making his Major League debut as a pinch-hitter. He flew out to right field against Brewers' reliever Michael Blazek for the second out of the inning.
The 25-year-old was hitting .306/.375/.508 with 10 home runs, 59 RBIs and 47 extra-base hits in 102 games with El Paso.
Dickerson, the Padres' No. 13 prospect, is a San Diego native who is from nearby Poway. He was acquired from the Pirates in November 2013 for outfielder Jaff Decker.
Dickerson's manager for much of the season in El Paso was current Padres interim manager Pat Murphy.
"I couldn't be happier for a young man making his debut," Murphy said before Thursday's game.
Murphy was impressed with Dickerson's play a year after he was limited to just 41 games. Dickerson played 86 games in the outfield but has played some first base.
Dickerson suffered a severely sprained left ankle in Spring Training 2014, an injury that led to the discovery that he had cyst on the bone on his left heel. He later had surgery to remove the cyst.
"He's succeeded at every level," Murphy said. "He can swing the bat. He's not afraid. He can hit lefties as good as he can righties. He believes he can hit."
As for Venable, he becomes the second Padres player in the past week to require paternity leave.
Pitcher Ian Kennedy went on leave on Saturday and returned on Tuesday after the birth of his daughter, Evelyn Nicole, on Friday. He wasn't there for the birth, but he watched it on FaceTime from Miami.
According to baseball's collective bargaining agreement, players are allowed up to three days for paternity leave.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.