The 27-year-old skipper sustained the injury in the recent defeat at West Brom and following a scan he now requires an exploratory operation to determine the full extent of the damage.
Stock, who won his first Wales cap when playing the full 90 minutes against Russia earlier this month, will miss Saturday's derby clash at Scunthorpe, Tuesday's home match with Swansea and then successive games against South Yorkshire rivals Sheffield United and Barnsley.
Rovers boss Sean O'Driscoll has described the loss of his skipper as "a massive blow".
He said: "I think once they've gone in, they've decided to do one or two things with it, rather than waiting any longer, so the prognosis is that - in a best-case scenario - he will be out for three months.
"It's a massive blow. He's been playing with his ankle for some time and it was steadily getting worse and worse and worse.
"It came to a point where we had to do something about it, but we didn't realise it was actually as bad as it was.
"In hindsight, perhaps it was a good job that we did. We could have done it early, but when it became a problem that affected his training and games - with what the surgeons have said - it's just good that it was done sooner, rather than later."