There is also concern over his fellow Warrior and Scotland team-mate Huw Jones who picked up a toe injury. In the same game.
Steyn had surgery on Thursday and will be out for up to three months while Jones is awaiting results of a scan.
"Kyle is getting operated on so he'll be out for 10 to 12 weeks," said Franco Smith in The Scotsman. "It's an ankle injury. It might be a little earlier but it will be around then. Hopefully before Christmas we'll have him back training on the field and then we'll see how he develops.
"With Huw, we've had a mixed bag of feedback. We're waiting for the final outcome as more imaging was required. It's a particular one as it's his toe so we want to make sure that we get more clarity on that. It can be good news, or very bad news - we're still waiting."