Burish, who was injured in Tuesday's 6-0 loss to Florida when he was hit in the hand by a puck, is expected to miss four to six weeks.
The Stars also activated forward Steve Ott from injured reserve. Ott has missed the past six games with a hip injury. He is set to play in Friday's game at Colorado.
Stars coach Glen Gulutzan said Kari Lehtonen will get the nod in goal.
"For sure, Kari is going to go in goal tomorrow at Colorado," Gulutzan said. "We haven't set it completely in stone, but Rayzor (Andrew Raycroft) will come back here Saturday against San Jose. That's what our plan is right now. We haven't discussed it with [goaltending coach Mike Valley] and the goalies yet, but that's what is in my head right now."
Forward Krys Barch, who didn't practice Wednesday because of a twisted ankle, was on the ice Thursday, and Gulutzan said Barch is fine.
Mark Stepneski covers the Stars for ESPNDallas.com.