Bardsley sustained the problem early in pre-season and is set to be absent for "a number of weeks".
Boss Martin O'Neill revealed his defender had already gone under the knife but was able to deliver better news on injured trio Stephane Sessegnon, Wes Brown and David Vaughan.
"Phil Bardsley has had an operation," O'Neill said. "That's a real blow for us.
"Stephane has done a little bit of training and hasn't felt any effects. He hasn't been able to do that much but in the course of the next few weeks in terms of the sort of fitness level that he can attain we hope he gets there pretty quickly."
O'Neill added: "Wes Brown is feeling a bit better but obviously getting a bit annoyed that injuries have plagued him. David Vaughan's making progress and he had an operation on his side to cure a problem and he's making good progress out there on the training field but hasn't joined in with us yet."