But the 26-year-old is hopeful of being fit in time for the Rugby World Cup, which starts in September.
It means that Maitland has played his last game for Glasgow as he is joining London Irish next season.
Maitland picked up the injury during Warriors' 20-15 European Champions Cup defeat by Bath in January.
Warriors head coach Gregor Townsend said: "Sean Maitland, who has worked really hard during his rehab, got some tough news last week when it became clear that his shoulder would require surgery.
"The operation at Spire Murrayfield Hospital was a success and he's targeting to be back for the Rugby World Cup.
"I'd like to take this opportunity to thank Sean for his contribution to the club.
"He's been an excellent player for us and we wish him well at the Rugby World Cup and also next season at London Irish."
Maitland, who has 15 Scotland caps, had initially hoped to return to action during the Six Nations campaign but broke down during training.
Glasgow lead the Pro12 table with four games remaining and he will miss the play-off semi-final and final should Warriors progress.
The New Zealand-born back, who can also play on the wing, has made 40 appearances for Warriors and scored 10 tries since joining from Canterbury Crusaders in 2012.
Glasgow Warriors and Scotland full-back Sean Maitland will miss the rest of the club season after undergoing shoulder surgery.