The 21-year-old had been touted as a possible replacement for Conrad Jantjes after the Boks' first-choice full broke his leg last weekend.
Steyn had also been seen as an option at fly-half or inside centre but he will now be pushed to return to fitness for the start of the three-match series against Ian McGeechan's tourists.
"We are awaiting the results of the scan, but Francois is likely to be out for six to eight weeks," said Sharks coach John Plumtree.
"He has the same injury that Ruan Pienaar has just recovered from."
Pienaar, the current incumbent of the Boks' No10 shirt has recently returned from injury along with the likes of Bryan Habana and Juan Smith, but players of the calibre of Jean de Villiers and Andries Bekker are serious doubts for the opening international in Durban, while Jantjes and Bath fly-half Butch James are definitely unavailable.
Other Springbok squad members currently facing indefinite but less lengthy spells on the sidelines include scum-half Fourie du Preez and star flanker Schalk Burger.
Both will miss the weekend's Super 14 action with club doctors not yet giving a date for their likely return.