But the 26-year-old now faces another spell on the sidelines after picking up a fresh injury to his knee during defeat to Connacht in the regular season closer.
"We're disappointed for Alex that his season has been cut short through injury," said Glasgow boss Gregor Townsend.
"He had been playing very well and played a big role in getting us into the PRO12 play-offs.
"We wish him all the best with his rehab and we look forward to him returning to training ahead of the new season."
And prop Puafisi will also be missing from the play-offs after being given a three-week ban for his red card in the clash with Connacht.
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