Stanton said he tweaked his side while swinging during Saturday night's game against the Reds, and felt some discomfort when he played on Sunday.
He said before Friday's series opener in New York that the injury is not healing the way he hoped, and manager Ozzie Guillen doesn't expect to have him available until at least Sunday.
"He's not feeling good enough out there," Guillen said. "He couldn't do a few things we asked him to do, so we'll see how he feels for Sunday."
Stanton, batting .283 with 34 homers and 81 RBIs, tried to take swings this week but was visibly frustrated Friday and said he "didn't think it was going to react like this."
"It's not where I want, so I'm not going to aggravate it when [swinging] is the thing that hurts it," he said.