The club have said he will undergo a minor procedure in Portugal this Friday, and be out for four to six weeks.
The club's website has reported that he will undergo a minor procedure in Portugal on Friday.
The centre-half said: "I have been struggling with this on and off for some time and I've come to the point where it feels like surgery would help it.
"The recovery time is short so I hope to be back 100 per cent some time after the New Year."
The 31-year-old has made five appearances for the club so far this season, but hasn't featured for the side since the League Cup third round win over Hull City in September.
It is a bit of a blow for Alan Irvine's side with a busy fixture schedule ahead in the build-up to Christmas and New Year. Olsson is an experienced performer who can make it awkward for strikers when they turn up to the Hawthorns, but they have shown signs of good form with a couple of a stand-out performances without Olsson marshalling the defence.
As a result he will miss key fixtures against Arsenal and Manchester City amongst others - and the West Midlands derby against Aston Villa at The Hawthorns on December 13.