"Cliff's got a Grade 1 left external oblique strain, which is kind of what we thought it was going to be," said general manager Ruben Amaro Jr. "And he seems to be doing better and better every day. Hopefully he'll only miss a couple starts, but we'll see how it goes."
Lee is eligible to be activated next Friday night, when the Phillies play at Nationals Park.
"It's possible," Amaro said. "We'd like to have him miss only a couple starts, but if he has to miss three or four starts, that's what it will be. We've got to be cautious. I don't want to have this thing blow out and miss him for a longer time."
In other injury news:
Second baseman Chase Utley (chronic knee inflammation) remains in Arizona working with a physical therapist.
"He's going to be out there [Arizona] for another week or so and then we'll see where he stands," Amaro said. "But he seems to be progressing very well. When he gets to the point where he's feeling significantly more comfortable, we'll get him down to Clearwater [Fla.] and get him going."
Right-hander Michael Stutes also had an MRI on Thursday that revealed a mild rotator cuff strain. He'll be shut down for two to three weeks and report to Clearwater to continue his rehab.