The England international landed awkwardly during the Clarets' 1-0 victory against Crystal Palace last weekend.
Heaton is believed to be facing a layoff of several months, and on Thursday, Dyche admitted that he is not putting a time frame on the stopper's recovery as of yet.
"Tom's surgery went very well. Tom was good afterwards. I'll speak to him this afternoon," Dyche said in his press conference ahead of Burnley's Premier League trip to Liverpool.
"We're happy the surgery went well but we won't rush Tom back. He has to be 100% right, but this is just a blip and he'll be fine. As long as the surgery heals properly he'll be on top of rehab because he's ultra professional.
"They'd be a lesser period out for an outfield player but a goalkeeper is constantly landing on his shoulder. Tom understands the role and that it can happen. He's had a fantastic run. It won't be weeks, it will be a longer period."
Dyche also confirmed that free agent Anders Lindegaard is training with the Clarets, telling reporters: "Anders has spent days with us. We'll speak to him accordingly. We want three goalkeepers."
Heaton, used in all four of Burnley's Premier League outings this term, has rivalled Joe Hart for a starting spot at international level of late.