Dubnyk, a former first-round draft pick, was the Oilers' regular starting goalie until he began struggling in November and was partially supplanted by Ilya Brygalov.
The 27-year-old goaltender, in his fifth NHL season, has a .894 save percentage and 3.36 goals-against average in 32 games this season, including 29 starts.
Dubnyk is expected to provide a veteran presence for the Predators, who are awaiting the return of injured goalie Pekka Rinne (hip infection). Rookies Marek Mazanec and Carter Hutton have been sharing time in net.
Going to the Oilers is fifth-year veteran Hendricks, who has two goals and four points in 44 games for Nashville this season.