Ducks general manager Bob Murray announced Thompson's injury Tuesday.
Thompson tore his tendon while working out last week, and he underwent surgery to repair it. Murray says he doesn't expect to see Thompson back in uniform before the trade deadline, which typically falls around March 1.
Thompson is a valuable depth-line forward for the Ducks, who won their fourth consecutive Pacific Division title this season.
He had three goals and three assists in 49 games after missing the first 26 games of the season recovering from surgery on a torn labrum in his shoulder.