Steyn, who can also play at centre, has been in fine form for his club who are fighting for a play-off place in the United Rugby Championship.
They face the Bulls in Pretoria at altitude on Friday as they look to end their mini-tour of South Africa with a victory.
“Kyle Steyn is definitely out [of Bulls games],” said Danny Wilson, the Glasgow coach. “He has an Achilles injury but it’s not quite as black and white as that. It’s the ligaments in that area and we are trying to nail down what it means.
“It’s a medium term injury, and hopefully not long term, but it’s unlucky for Kyle who’s been in really good form and was really looking forward to playing back in South Africa but only lasted around 10 minutes.”
Steyn, who was player of the match in Glasgow’s win over Newcastle in the Challenge Cup recently, has had the injury scanned and is due to see a specialist to assess the extent of the damage. There could also be repercussions in terms of his availability for Scotland’s summer tour of Argentina.
In the meantime, Ratu Tagive has flown in from Glasgow to join the Warriors squad and will provide wing cover for the Bulls game.
“It’s definitely a medium termer but whether we see Kyle again this season, we’ll have to wait and see but at the moment it’s doubtful,” added Wilson who has not had his troubles to seek of late in terms of injuries.
Sam Johnson, the Scotland centre, also had to come off against Stormers, with an ankle problem, and faces a race to be fit to face the Bulls.
“Sammy Johnson picked up a niggle and we’re still trying to see what that means for him for this weekend,” said Wilson. “When you add to that Matt Fagerson, Scott Cummings, Rufus McLean, George Horne – these are big international players who you really want to have going into the business end of the season.”
Leinster are out in front in the URC but with only four points separating the seven teams that occupy the places between second and eighth there is little margin for error as the league enters its final two laps. Glasgow have been in the top four for most of the season but last Friday night’s loss to the Stormers saw them drop down to sixth.
Only the top eight qualify for the play-offs and Wilson knows he needs to be wary of a late surge by the Scarlets, who are currently ninth, seven points behind Glasgow, and whose final two games are against Ospreys away and Stormers at home.
“This league is so tight,” said Wilson. “You’ve got the top nine teams battling for those eight places and we’ve been in the top four for the majority of the season and then we come to this really tight business end and we can quite easily, with one or two losses or not picking up points, or the other way around with a couple of wins, jump [or fall] three or four places.
“The league can change very quickly over a few games and for us, with a series of away games, it’s a big challenge.”
Glasgow’s final match of the regular URC season is against Edinburgh at BT Murrayfield on May 21 and Wilson knows that anything they can take from the Bulls game could have a huge bearing on their play-off hopes after they came away empty-handed in Cape Town.
“We knew coming here we’d have to get points. It’s a very, very tough place - not many teams will come here to South Africa and take points, especially against the Bulls and the Stormers.
“I think we’re all learning the lessons of coming to South Africa and playing these sides. In the past we came here and played the Southern Kings and the Cheetahs [in the Pro14] and no disrespect to them because they were good sides, but maybe not with the firepower that these guys have got.
“So you’ve got the challenge of coming to South Africa and everything that brings and then you’ve got some quality rugby teams. It’s great for the competition and it’s great to raise our standards. We know when we come here we’ve got to be at the top of our game and hopefully we can make some improvements going into game two.”