The New Zealander was forced off with the problem during last weekend's 1-1 Barclays Premier League draw against Birmingham and manager Steve Kean revealed there was no option but for Nelsen to go under the knife.
Kean said of the operation: "It went well. The surgeon was happy about it and he had a full clearout. There were a lot of little bits of floating debris in his knee that he's been in a lot of pain with. He couldn't manage to go on. We're hopeful he'll be back in time for pre-season."