Wood went six innings, allowing three runs on five hits, but did not factor into the decision in the Dodgers' 6-5 victory over the Pirates in 12 innings Monday. He gave up three home runs for the second time in his 134 major league appearances.
Manager Dave Roberts said Wood is experiencing inflammation in the sternoclavicular joint in the front of his pitching shoulder, an issue that Wood has had in the past, including in May, when he was placed on the 10-day disabled list for the injury.
"We'll make a decision once the medical staff puts an eye on him," Roberts said. "It's a little concerning considering his history. ... We really have got to be cautious."
Wood is 14-1 with a 2.41 ERA and 127 strikeouts in 123 1/3 innings this season.
Kershaw, who leads the National League with 15 wins against just two losses, has been sidelined since July 24 with a back issue. He threw four simulated innings on Monday, and is scheduled to make a rehab start Saturday for Triple-A Oklahoma City.
Information from The Associated Press was used in this report.