If O'Driscoll is ruled out for the coming weeks he would also miss the Magners League games with Connacht and Edinburgh but would return in time to lead Ireland out against South Africa on November 6.
Leinster coach Joe Schmidt said: "We don't know for sure but I don't think it's going to be as bad as we first feared.
"When I first saw him come off I thought it was four to six weeks straight away. He might only be out for two or three weeks, maybe four weeks, although this is still only an estimate at the moment.
"We'll do some more tests and get a clearer picture.
"As much as he was delighted that we managed to get a win, individually he was really disappointed because he is really keen to see the job through."