The 31-year-old will likely miss six to seven months of action, according to manager Derek McInnes.
Reynolds sustained the injury in a pre-season game with Cove Rangers, and travelled to Glasgow for the operation on Thursday.
McInnes told Aberdeen’s website: “It’s extremely disappointing that our worst fears were confirmed last night when he went into surgery.
“We’re going to be without him for the next six or seven months so it’s a huge blow especially when these things happen in a pre-season game, but injuries are part and parcel of that. Knowing the character that Mark has, we’re hoping his rehabilitation will be as straight forward as possible.
“We’re disappointed for ourselves because we’re missing an important player, but we’re disappointed for Mark because he had worked extremely hard during the close season to give himself the best chance of being that important player he has always been for us.
“Unfortunately, he’s going to have to take a back seat now and work hard with the physios but I wouldn’t bet against him coming back as strong as ever.”
Reynolds’ injury could increase Krystian Nowak’s chances of landing a deal at Pittodrie. The former Hearts defender has been on trial with the Dons but a combinationof abandoned and cancelled pre-season fixtures has limited his gametime, and McInnes is keen to see him play against Arbroath this weekend.
Speaking to the Evening Express, McInnes said: “We have not really had the opportunity to see [Krystian] in action, although he got 20 minutes or so against West Brom.
“We have invited him to stay with us this week and play in the game on Sunday, then we will sit down and make a call on that after the game.”