According to baseball's collective bargaining agreement, players are allowed up to three days for paternity leave.
To take Kennedy's place on the roster, the team recalled right-handed reliever Leonel Campos from Triple-A El Paso.
The team also announced Saturday that it reinstated catcher Tim Federowicz from the 60-day disabled list and then designated him for assignment. The Padres had to make a roster move with Federowicz on Saturday, as his allotted 20 days on a Minor League rehabilitation assignment had expired.
Federowicz had surgery in March to repair a meniscus tear in his right knee. Given a three-to-six month window of recovery, Federowicz returned to the field last month. But he hit .222 in 63 at-bats with Class A Advanced Lake Elsinore and El Paso.
Federowicz, acquired from the Dodgers in the Matt Kemp deal in December, would have likely made the Opening Day roster as the backup catcher before getting hurt.
"The combination of Derek and Hedges certainly played a role in our decision on Tim," said Padres assistant general manager Fred Uhlman Jr. "We want Austin to play and get at-bats and get experience. He's done well here. Our pitching staff likes throwing to him as well as Derek. We felt the best combination of catchers right now was Austin and Derek."
Campos, who made his big league debut with the Padres last season, was 2-0 with a 2.37 ERA in 49 1/3 innings at El Paso. He had 68 strikeouts in that stretch and had allowed just 28 hits.
Campos had a 5.41 ERA in six games and seven innings with the Padres last season.
New reliever Marc Rzepczynski also reported to Marlins Park on Saturday. The Padres traded outfielder Abraham Almonte for him on Friday in a deal with the Indians.
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.