The former Dundee United star suffered the injury earlier in the season, but has only now gone under the surgeon's knife.
"Stevie had the operation we expected he needed." Gers boss Alex McLeish told the club's official website.
"We've spoken to the surgeon and he was very happy with the procedure.
"It's now a case of rehab for Steven.
"The prognosis is three to six months so we will expect him back after six months and if we get him back before it will be a bonus."
Meanwhile, McLeish also confirmed that defender Craig Moore is to see a specialist about his injured hamstring - which he picked up against Celtic on Saturday.
"At half time Craig complained that he had no sprint," McLeish said.
"He was finding it difficult to accelerate when closing down or pushing forward with the ball so we took him off.
"As far as I am aware there is no strain or pull in his hamstring but we will have to get the advice of someone other than our own medical team on this one.
"Craig will see a specialist about this problem and hopefully we can resolve it once and for all."
