Steyn hasn't played since picking up a lower leg injury against Benetton in September but the initial diagnosis was positive and the winger was expected to feature in South Africa.
However, the injury is worse than initially thought and the Glasgow skipper could possibly be out of action for between six and eight weeks, ruling him out of the four Scotland games in the Autumn Nations Series.
"Unfortunately, Kyle withdrew yesterday," Glasgow head coach Franco Smith told The Scotsman. "We scanned him on Monday, then scanned him on Wednesday when we got here. And it looks like it's more serious than we thought originally.
"It will then become a six-week, six to eight-week injury. But the confirmation will come on Monday, so that will be more clear. But for now, he's not available for this game and most likely not for next week either.
"I think it will be a disappointment. We need confirmation also from the doctors in Scotland next week and the week after with this precise plan. We will obviously make sure that we get him back on the field as soon as possible.
"But I do not want to rule anything out for him at this moment. It's a subtle injury that can be treated conservatively. So we'll just see how he progresses. But it looks like it's a little bit longer term than just two weeks."