"He will sadly miss the rest of the season," Rangers said in a statement on their website on Tuesday.
"Steven will be seen by the same surgeon who successfully treated him in 2008 and his rehabilitation programme will be 8-9 months."
Naismith is the top scorer with nine goals in the Scottish Premier League this season, his strikes helping the Glasgow club open up a nine-point lead at the top after just 13 games.
City rivals Celtic are 12 points off the pace in third.
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