The 34-year-old midfielder sees a specialist today to discover the full extent of the damage to his knee sustained against Kilmarnock.
Robson is definitely out of the clash with former club Celtic on Saturday, which is heading for a sell-out following Aberdeen's superb start to the season.
But manager Derek McInnes fears that Barry Robson will miss several more matches.
McInnes said: “We expect to be without Barry for a few weeks. He has had the injury scanned and will see a specialist on Wednesday.
"It's not what we or Barry wanted but we just have to get on with it.
"He made a very strong debut against Kilmarnock and we hoped he would build on that but it wasn’t to be.
"Injuries happen, though, and all we can hope for now is that he gets back to fitness sooner rather than later.
"But it is a blow to lose him for the next few games."