Kershaw, 8-8 with a 2.89 ERA, ran into an auxiliary scoreboard in Dodger Stadium while shagging fly balls during batting practice.
"I wish it didn't happen. It was one of those freak things. I feel bad. I kind of feel like I'm letting the team down a little bit by missing a start," said Kershaw, whose ERA is ninth in the NL.
"It is obviously pretty disappointing. It's really frustrating, too. At the same time, it is what it is. I just have to get better now."
The Dodgers did not immediately announce their starter Friday, when they open a three-game series at San Francisco.
Left-hander Randy Wolf, scheduled to start Saturday, is a likely candidate. Dodgers manager Joe Torre said he planned to use a six-man rotation this week after the recent acquisitions of Vicente Padilla and Jon Garland, so Wolf would be pitching on five days' rest if he started Friday.
Asked if he will miss only one start, Kershaw said, "that's the plan. It's my right shoulder, so whenever I can tolerate the pain, I'll be good to go."
Kershaw collided with the fiberglass edge of a field-level scoreboard.
"There's no issue throwing-wise. The only issue for me is if he reaches for a ball," Torre said.
"I wasn't running really hard, but at the same time if you don't something is there and you run into it, you don't brace for it at all," Kershaw said.