Connolly lasted just 30 minutes of The Dons' encounter against Swindon on Saturday before hobbling off with a knee injury.
The Republic of Ireland marksman was making his first appearance of his club's pre-season build-up but left the ground on crutches.
Dons boss Stuart Murdoch admits he is uncertain how serious Connolly is injured but acknowledged picking up knocks was one of the pitfalls of playing pre-season friendlies.
"We're not sure how bad it is at the moment, but we'll know in the next couple of days," said Murdoch.
"That's the thing about pre-season games, you don't want to lose players."
