Kershaw is expected to start Friday in the Freeway Series opener against the Los Angeles Angels, Dodgers manager Don Mattingly said during batting practice.
Mike Bolsinger (5-3) stepped in for the start against the A's.
"Clayton went through his (bullpen session) the other day and was fine during that, but he felt a little sore the next day," Mattingly said. "I thought he'd be ready to roll (Wednesday), but (Tuesday) it wasn't that great. He was still a little tender. So with the off day (Thursday), we didn't think there was any reason to push it. We'll try to take advantage of the off day, and hopefully we're good on Friday."
Kershaw has pitched 29 consecutive scoreless innings after taking a perfect game into the seventh inning of a win over the New York Mets last week. He has thrown two shutouts in his past three starts with 38 strikeouts and no walks, making him the first pitcher in history with three straight scoreless starts that included no walks and at least 10 strikeouts.
After winning the NL MVP and Cy Young awards last season along with his fourth straight ERA title, he is 8-6 with a 2.51 ERA this season. He also leads the majors with 185 strikeouts.
"Obviously, we're going to continue (to monitor him)," Mattingly said. "If he's not 100 percent Friday, we're not going to do it then, either. But as of right now, he's scheduled for Friday."
Bolsinger hadn't pitched since July 22, when he yielded one unearned run over seven sharp innings in Atlanta. The right-hander lowered his ERA to 2.79 while giving up just three earned runs in 17 innings over his past three starts.