Kiermaier will have an MRI exam Monday, with a trip to the DL appearing likely.
"I don't want to get too far ahead of it, but he's going to be out," Rays manager Kevin Cash said. "There's a chance he's going to miss a chunk."
"I don't think the odds are in my favor, to be quite honest," Kiermaier said.
Kiermaier suffered the injury in the bottom of the first inning when he slid headfirst into second base while advancing on an error by Phillies left fielder Rhys Hoskins.
After being examined on the field, Kiermaier initially remained in the game as a baserunner before ultimately being replaced by Johnny Field in the top of the second inning.