Robson missed last weekend's 3-1 win over Motherwell and travelled to England to see a specialist.
Manager Derek McInnes said on the club's official website: "Barry Robson is out. He is down south today having surgery to explore what the problem is with his injury.
"We don't think it is anything too serious but it will be enough to keep him out for a few weeks."
Robson will miss the visit of former club Celtic on Saturday lunchtime in a match that has captured the imagination of the Aberdeen fans following their opening two Scottish Premiership wins. But McInnes is eager to avoid the hype.
"Like everyone else, the players and myself are looking forward to the game," he said. "It is a fantastic game to be involved in.
"Obviously there is a lot of excitement about it and that is the way you want it to be. For us though it is just about being professional and going out and doing a job.
"The excitement is for everyone else. I am so grateful to the supporters for the way they have responded and bought so many tickets and believed in what we are trying to do here.
"All the hype is for the fans and the media. You would rather people were talking up the game than being negative about it. I hope this is the start of something special and I believe we can be successful but how quickly that happens remains to be seen."