The 32-year-old was unable to play in Monday's 1-0 defeat at home to Charlton Athletic, and exploratory surgery has now identified and corrected the injury.
The former Rangers captain will now embark on a recovery programme, meaning the big Italian will be out for up to three months.
The news will come as a blow to Rovers boss Graeme Souness, with his side currently struggling for form at the moment.
With his backline ravaged by injury, illness and suspension, Souness will likely have to turn to the likes of Andy Todd for the away match at Southampton on Saturday.
