Habana was carried off on a stretcher in the second half after being tackled by Sam Cane and falling awkwardly. Coach Alistair Coetzee told reporters the player faces at least 10 weeks on the sidelines.
That means he will only return if the Stormers reach the playoffs, a bitter blow to their chances.
With Habana set to join French Top-14 side Toulon at the end of the Super Rugby campaign, he could have played his final match in the competition he won with the Bulls in 2007 and 2009 before moving to Cape Town.
The win by the Stormers was their first in the tournament this season.