The Scotland right-back suffered the injury in training and has not played a minute of his club's pre-season programme.
Black Cats manager Martin O'Neill said: "Phil Bardsley has had an operation. That's a real blow for us."
The manager's preparations for the season have been hampered by a number of injuries, with David Vaughan also recovering from surgery and both Wes Brown and Stephane Sessegnon struggling.
O'Neill said: "Stephane has done a little bit of training and hasn't felt any effects. He hasn't been able to do that much but we hope he gets there pretty quickly.
"Wes Brown is feeling a bit better but obviously getting a bit annoyed that injuries have plagued him.
"David Vaughan's 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."