Jason Lane, who made two appearances with the team earlier this season, will join the team for a spot start in the series finale at Turner Field.
San Diego manager Bud Black said, "We think it's a one-start thing," adding that Kennedy could slide into the rotation either Friday or Saturday at Petco Park against the Braves. He'll throw a side session on Tuesday or Wednesday.
Kennedy won his eighth game of the season Wednesday, holding the Cubs to three runs over six innings at Wrigley Field. He suffered the injury to his oblique, not making a pitch, but taking a swing, Hinch said. The injury was so minor that Black said that if he really had to, Kennedy could have started Monday.
In fact, Kennedy has been able to play catch on the side in Atlanta this weekend.
Instead, the Padres will be cautious with Kennedy who has thrown the second-most innings on the team (135 2/3) this season, making all of his 22 starts to this point, posting a 3.66 ERA.
Kennedy's injury was announced by Hinch to erase any speculation that this might have to do with him being on the trading block in advance of Thursday's non-waiver Trade Deadline.
"He's a well-sought after pitcher … because of his talent and years of control and what he can bring to a team," Hinch said. "Whether we continue to discuss him or are open to moving him … will lead into the Deadline. I don't really want to comment on his trade status. Teams like him, we like him.
"But this particular reason for not having him pitch has to do with what's best for the player."
Lane, 37, tossed 4 1/3 scoreless innings over two games with the Padres in June. He has a 4.67 ERA with Triple-A El Paso this season in 19 starts. Lane spent seven seasons in the Major Leagues as an outfielder with the Astros and Padres from 2002-07.
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.