The teenage centre-back, who has been loaned from Championship club Middlesbrough, has been plagued by the problem for a number of weeks and missed Rovers' 2-2 draw with Portsmouth last Saturday.
Gibson saw a specialist on Thursday and they confirmed the injury is set to keep the defender out of action for the duration of his stay.
With Gibson originally scheduled to return to Teesside at the start of January, Rovers boss Ronnie Moore admits he is now likely to head back to his parent club for treatment.
"We've just got to wait," Moore told Tranmere Player.
"He's been to see a specialist and it looks like he'll be out for six to eight weeks which would be a nightmare.
"They think it's an abductor problem.
"He's in today (Thursday) and we'll have a chat to him and I'll speak to Tony Mowbray about the situation.
"We've got him until January and he'll obviously go back and get treatment and they'll look after him and we'll take it from there."