Kennedy will be followed by Tyson Ross on Saturday and Odrisamer Despaigne on Sunday. The team is off on Monday before opening a three-game series in Chicago against the Cubs on July 22.
Black said it's likely that Eric Stults will start the first game of that series before the team goes back to Kennedy for the middle game.
The Padres will not need a fifth start until July 26 against the Braves, which is when they'll likely swap in rookie Jesse Hahn, who was sent to Triple-A El Paso on Saturday, a roster move made essentially so the team can curtail his workload.
Hahn has thrown 79 innings this season between Double-A San Antonio and the big leagues. The Padres won't likely allow him to double the 69 innings he threw last season while in the Rays' system.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.