"Tom's surgery went very well. I'll speak to him this afternoon," Dyche told a news conference ahead of Burnley's Premier League trip to Liverpool on Saturday.
"We're happy the surgery went well but we won't rush Tom back. He has to be 100 percent right, but this is just a blip and he'll be fine.
"They'd be a lesser period out for an outfield player but a goalkeeper is constantly landing on his shoulder. He's had a fantastic run. It won't be weeks, it will be a longer period."
Burnley are left with only Nick Pope and new signing Adam Legzdins as goalkeeping options and will look to recruit cover for the injured Heaton.
Dyche said former Manchester United goalkeeper Anders Lindegaard, who is a free agent after being released by Preston North End in May, is training at the club.
Free agents can be signed by a club at any time during the season, if they had been released by their previous club before the end of the transfer window.
"Anders has spent days with us. We'll speak to him accordingly. We want three goalkeepers," he added.
Burnley have made a good start to the season after picking up two victories in their first four league games.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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