Sutherby was evaluated Monday after getting hit in the shoulder during the second period of Sunday's 4-2 loss to Phoenix. He did not return.
"We're hopeful that he'll react to treatment from our trainers and be back before the [Winter Olympics] break," Crawford said.
Sutherby, 27, has six points, four of them goals, in 32 games played for the Stars. He has had back issues and missed seven games in November because of it. He's also been a healthy scratch for a handful of games. The former first-round pick of Washington in 2000 has played on the fourth line for most of the season.
Warren Peters was called up on Monday from the Texas Stars, Dallas' primary AHL affiliate, to give the Stars some more forward depth with Sutherby out.
Richard Durrett covers the Dallas Stars for ESPN Dallas.