Danks went on the 15-day disabled list retroactive to May 20 after feeling an abnormal soreness in the back of his left throwing shoulder following a start on May 19. He made a rehab start for the Triple-A Charlotte Knights on June 12, allowing one earned run in four innings, and felt soreness again.
Danks had an MRI done when he first suffered the injury and had another one on Tuesday.
"That was my first question (about surgery)," Danks said following Monday's game. "When you hear tear, it's kind of scary. I don't think it's anything super major. Like I said, I went out there and pitched earlier last week and felt fine, stuff was great, just having trouble bouncing back. This is the reason.
"Get some rest and get back at it. I don't know any schedule at this point or anything. It's frustrating because it feels good one day and it feels like the crap the next day. It is frustrating, but at the same time it's good I actually know what we're dealing with now."
Danks has a 3-4 record with a 5.70 ERA for the White Sox this season. Rookie Jose Quintana has replaced him in the rotation and is 2-1 with a 1.53 ERA in 35 1/3 innings.
Danks received a five-year, $65 million contract extension in the offseason. He'll make $8 million this season and $14.25 million from 2013-16.