Bourque scored a goal on two shots in Friday's 6-4 loss to the Panthers in Finland.
Bourque provided an assist in Tuesday's 4-2 loss to the Sabres.
Bourque (undisclosed) will be in action against San Jose on Tuesday, Brian Rea of Bally Sports Southwest reports.
Coach Peter DeBoer hopes that Bourque (undisclosed) is able to play this weekend, despite the forward missing practice Friday, Lia Assimakopoulos of The Dallas Morning News reports.
Bourque (undisclosed) was placed on the injured non-roster list Monday, Stars radio analyst Bruce LeVine reports.
Coach Pete DeBoer said Monday that Bourque (undisclosed) is doubtful for Opening Night against the Predators on Thursday, Stars radio analyst Bruce LeVine reports.
Bourque (undisclosed) practiced Tuesday without limitations, Sam Nestler of DLLS Stars reports.
Bourque (undisclosed) didn't practice Saturday because of a minor injury, per Sam Nestler of DLLS Stars.
Bourque was called up from AHL Texas on Wednesday.
Bourque was reassigned to AHL Texas on Thursday.