The 19-year-old damaged ankle ligaments in the Scottish Cup quarter-final win over Motherwell.
Aberdeen boss Craig Brown said: “The good news is there’s nothing broken but the bad news is Fraser will be out for three or four weeks. That means he will be struggling to make it back in time for the semi-final which is a blow for us and the player.
“Fraser has been in great form for us this season and it would be cruel if he was to miss out on that big match.
“It’s also a nightmare for us as we have so many midfield players out injured at the moment and of course Gavin Rae is ineligible for the Cup.”
