The 35-year-old, who signed a new one-year deal in March, has made only eight appearances in all competitions this season, with Matt Lowton making the position his own, but has waited for the right time to go under the knife.
The former Manchester United youngster will therefore join Robbie Brady - who will be out of contract in the summer - and Kevin Long in being unavailable for the rest of the season.
Boss Sean Dyche said: "We've got a couple of situations where players will miss games because of injury, that have been hanging on...Phil Bardsley has got a hernia situation, he has been keeping himself right, training very hard to make sure we saw the job through, and that will need doing now.
"A couple of others have thinks being looked at just to make sure. We have to get on top of them because obviously we can't keep going with these injuries and go into next season with them."
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Nick Pope is being monitored after the shoulder injury which kept him out of the games against Newcastle United and Manchester United, but Brady and Long won't feature again this term: "Popey has had a couple of niggles with his shoulder and knee so we will wait and see on him. They are the same issues, we have just been keeping an eye on him.
"Robbie Brady is not going to be right, Kevin Long is not going to be right."