Kuroda, 38, was flown back to New York for an MRI, which according to manager Joe Girardi revealed no tears or structural damage.
"It was the best news we could have received," Girardi said.
Still, Kuroda, who has been the team's best and most consistent starting pitcher this season, will not be able to go when the Yankees open a three-game series against the Baltimore Orioles at home Friday night. He will be replaced by Ivan Nova.
"We'll re-evaluate him on Friday and see where we decide to slot him," Girardi said.
Kuroda (7-6, 2.95) first experienced the soreness while warming up before his start Sunday night against the Orioles, a 4-2 Baltimore victory in which Kuroda took the loss.
"He was a little tender after the game on Sunday," Girardi said. "But he said he felt better today, so that's good news."
Girardi did not rule out the possibility of a trip to the disabled list -- the Yankees have already had 14 players on the DL this season, including eight who are still out of action -- but identified his concern level as "low" due to the favorable MRI report.
"If the MRI comes back and you see something, obviously you're going to be concerned with a pitcher that it's going to be a while," he said. "But the fact that it came back negative makes you feel good."