Kennedy left Thursday's home opener in the third inning.
Also Friday, the Padres selected the contract of left-handed reliever Chris Rearick from Triple-A El Paso and recalled right-handed reliever Brandon Maurer from the same club.
It's the first major league call-up for Rearick.
Right-handed reliever Nick Vincent was optioned to El Paso.
The Padres also transferred left-hander Cory Luebke from the 15-day to the 60-day disabled list. He's rehabbing from a second reconstructive elbow surgery.