Dobson was forced off with the knock in the first half of Sunday’s 22-10 win over Wakefield.
Head Coach Craig Sandercock said: “Michael suffered an injury to his shoulder during the game at Wakefield last weekend and was removed from the field as a precautionary measure.
“His injury requires nothing more than conservative management though and it looks likely that he’ll only miss the next month of football which is positive news for us. Being without Michael makes life tough for us, especially with the other injuries that we have, but I’ve always said that these kind of problems present opportunities for others and we’ll just get on with the job.”
Rovers are already without Dobson’s first choice half back partner Blake Green through injury.