The striker has been restricted by the problem for a number of weeks and was rested for the Clarets' game against Tottenham in December and also missed last Saturday's 3-0 defeat to Chelsea.
Clarets manager Sean Dyche said: "Hopefully he will have a smooth recovery.
"You don't like losing good players but, equally, it allows other players to come in and perform and that's what we'll be looking for them to do."
The club have not given any indication how long the player will be out but a normal timeframe would be two to four weeks, depending on the severity of the problem.
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