O'Driscoll's centre partner for club and country Gordon D'Arcy also went off with a calf problem while flanker Sean O'Brien did not even make the starting line-up with a similar complaint.
But ahead of a huge summer with the British and Irish Lions for O'Driscoll, who appeared in all five of Ireland's RBS 6 Nations games this year, any injury inevitably invites concern over the 34-year-old's durability.
"We will have a look at Gordon and assess him in the next 48 hours and find out the real extent of the problem. Brian's back tightened up and he couldn't fully stretch out," said Leinster coach Schmidt, whose side still have the Pro12 and European Challenge Cup finals to come this season.
"He wanted to carry on, but it wasn't really an option against a back line like Glasgow's. I wouldn't be too concerned, and I'm normally concerned about everything, so that's a good sign.
"We didn't want to risk playing Sean against Glasgow, but hopefully he will be alright by next Friday. I don't know we will be doing a lot in the first half of the week and we'll probably restrict our training to Tuesday and Wednesday.
"We will get the glue and sticky tape out so we can put a team together for Friday and the final the week after."