Giants manager Bruce Bochy said Leake injured himself in Atlanta during a routine between-starts workout. Bochy added Leake underwent an MRI to confirm the diagnosis.
"He thought it was a cramp, but it didn't go away," Bochy said.
Bochy said Leake "hopefully" will make his next start, but added, "I can't say for sure."
To a degree, the Giants can afford to be patient with Leake, 27. Due to Monday's scheduled off-day, they won't need a fifth starter until Aug. 15. They can push that date back further if Vogelsong receives more than one start.
Leake pitched capably in his Giants debut last Sunday at Texas, lasting 6 1/3 innings and allowing a pair of runs on Josh Hamilton's sixth-inning homer.