The 20-year-old was stretchered off during Aberdeen's League Cup win at Motherwell last week after going down in agony following an innocuous-looking challenge with Shaun Hutchinson.
Dons boss Derek McInnes said on Thursday: "Clark Robertson had his operation yesterday and unfortunately will be out for 12 weeks with cartilage problem."
The Scotland Under-21 international, who has made 66 first-team appearances, had a previous spell out with a knee injury.
McInnes said: "It's his other knee. It's something that has happened and we just need to get on with it and give him every support to get back."
Meanwhile, 17-year-old midfielder Craig Storie, who has made two first-team appearances, has joined League One Forfar on a month's loan.
McInnes said. "This loan spell will be a good experience for Craig, despite it only being short term. It will provide him with some game time before returning to us for the busy festive period."