Halkett was substituted after 25 minutes in Paisley and replaced by Christophe Berra.
Speaking to BBC's Sportsound programme after the 0-0 draw, Levein revealed the initial diagnosis, describing it as a "body blow".
"He's gone in for a challenge and it's opened up the medial side of his knee and it's damaged the medial ligament so he could be out for quite a while."
Loic Damour also went off injured but Levein confirmed his substitution was only precautionary.
Hearts have been plagued by injuries this season with key players such as John Souttar, Steven Naismith, Conor Washington and Jamie Walker all being ruled out for a significant part of the season.