The England international sustained the injury during Burnley’s 1-0 win over Crystal Palace on Sunday.
Heaton went under the knife on Wednesday and is likely to missing for around four months.
But Clarets boss Sean Dyche says Heaton will be given as long as required to get himself right.
“It’s successful in its immediacy. The surgeon is someone we have known for a while and did a good job. Tom was good afterwards,” Dyche said.
“Provided your body heals properly we all know to the extent that Tom’s professionalism goes and he is as good as they get so I think as regards rehab, as long as the surgery heals properly then I think he will be top of that. He is ultra-professional.
“We only have very rough guidelines on how long he is out. They vary depending on the body’s natural state with healing and how quickly you can strengthen.
“The first thought will be to get him as right a possible and back to where he was. So there is no thought of rushing him back.
"The early signs are very good.”
Dyche will put his faith in reserve keeper Nick Pope for Saturday’s clash against Liverpool at Anfield.
Pope came off the bench against Palace and Dyche insists the 25-year-old will not be fazed.
“It’s hard for some players who have to sit behind players,” said the Clarets boss.
“They should be developing within the group anyway and they are ready to come. Nick is a great example of that.
“He has been working with some top-class keepers. He has been improving all the time. We all know the main measure is when you play.
“Nick has been improving daily. He did well against Palace and now he has a chance to show what he can do. That’s a great opportunity.”
Burnley have also taken ex-Manchester United keeper Anders Lindegaard, who is a free agent, on trial with the view to a short-term deal.
“He has come in to spend a few days with us and see what we do,” Dyche added.
“Ideally like any manager you want three goalkeepers and maybe a younger keeper under that. So that’s what we are looking to do if we can.”
