McKenzie is the latest addition to a growing casualty list at Rodney Parade and adds to Paul Turner's woes as his side sit just one place off the bottom of the league table after struggling so far this season.
"I picked it up in pre-season and was advised to have the operation," said McKenzie.
"There is not a lot I can do about it, but I hope to be back around Christmas time or soon after."
The Dragons travel to play Benetton Treviso tomorrow and will be looking for their second victory of the season before they break for the European Cup.