Trainer Stan Conte said Kuroda is progressing, but still "showing symptoms" from the oblique strain, which is not an injury "to push through" because it can linger for months.
"They are notorious for coming back," said Conte.
Kuroda's discomfort is on the left side of his rib cage, typical for a right-handed pitcher, according to Conte. Kuroda was allowed to play catch Monday, but Conte said he backed off Tuesday and Wednesday pending an examination by Dr. Neal ElAttrache before Wednesday night's game.
Kuroda, the Opening Day winner, was scratched before his scheduled start Saturday in Arizona and replaced by Eric Stults, who beat the Diamondbacks and will start again Thursday night.
The longer Kuroda is out, the more likely he will need a Minor League injury rehabilitation assignment before coming back. If nothing else, said manager Joe Torre, Kuroda would need a bullpen session and a simulated game, so his return is more likely weeks away than days away.
"He'll certainly need game situations," said Torre.
Tuesday's day off allowed Torre to juggle his rotation and push back rookie James McDonald, who is tentatively scheduled to start Sunday, but is in the bullpen in the meantime.
Torre said Wednesday that he will use McDonald as needed before Sunday and piece together that game with relievers if McDonald cannot start. Monday is a day off.
Conte said that disabled pitcher Jason Schmidt threw a five-inning, 73-pitch game in extended spring training on Wednesday. If he comes out of it healthy and is able to throw a bullpen session Friday, at least one more extended spring outing is likely before he would begin a Minor League rehab assignment.
"A lot depends on how he feels," said Conte. "He sounded encouraged."
Conte said that often-injured infielder Tony Abreu is now walking without crutches two weeks after suffering a bad ankle sprain. He could be sidelined another month.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.