The slugger said he tweaked his side on a swing during Saturday night's game against the Reds.
Stanton played on Sunday, but he felt some discomfort. Rather than risk anything, Stanton was out of the lineup for the series opener against the Braves at Marlins Park.
"Just taking a day," Stanton said.
Miami manager Ozzie Guillen didn't rule out sitting Stanton on Tuesday, as well.
"He has a little soreness in the oblique, rib cage," Guillen said. "He has been dealing with that for a little while. You have to be really, really careful about it because that thing can go for weeks. We're going to go by ear and see how he feels in the next couple of days, and from there we will make a decision on when he is playing or not."
Stanton didn't taking batting practice on Monday, opting to completely rest his side. Justin Ruggiano played right field in place of Stanton on Monday.
Stanton is batting .283 with 34 homers and 81 RBIs. The All-Star is second in the National League in home runs behind Ryan Braun of the Brewers (40).
Catching Braun already is a long shot for Stanton, who is one ahead of Cincinnati's Jay Bruce for second place in the NL.
"I'd rather him miss two games than miss the rest of the season, because that injury really can put you down for a little while," Guillen said. "That's why I think not playing him for a couple of days and all of a sudden we play him and boom he is done for the season. I don't think it's worth the risk to do that."