Steyn hasn't played since picking up the injury against Benetton in September but travelled to South Africa as the initial diagnosis was positive and the winger was expected to feature against the Sharks and/or Stormers.
Speaking ahead of the meeting with Stormers, head coach Franco Smith told Scotland Rugby News: "He (Steyn) was operated on on Wednesday afternoon. They put a little block on his fibula and it's a six-to-eight-week injury.
"It would have been the same time length [if he'd not had the op] so we decided to get it done properly to make sure he's available and healthy for the derbies at least, then going into the Six Nations."