Midfielder Cavanagh had been scheduled to return for the weekend win over local rivals Bury after serving a three-game ban, but missed out because of tendonitis.
"In the last couple of weeks Peter has been saying that he hasn't been able to function 100 per cent and while he's not in a great deal of pain, he has been getting aches and soreness," Dale physio Andy Thorpe told the club's official website.
"We sent him for a scan and it showed disruption in his Achilles. After seeing the surgeon, he has been told that he it will need up to six weeks to heal, which is obviously a blow for him and us.
"Taking time for it to heal is important because if he was to carry on then the disruption could develop into more and he could get a complete rupture. We don't want to go down that road, so we're taking the best possible option we can.
"Running is completely out of the question at the moment, but he is taking part in non-weight bearing exercises like bike work and swimming to keep his fitness up."