Hasek, 42, made 13 saves in Detroit's 3-2 win over Vancouver on Wednesday. He is 4-2-1 this season with a 2.68 goals-against average.
The Red Wings called up Jimmy Howard from their Grand Rapids AHL affiliate to back up Osgood. Howard is 3-1-0 with a 3.00 goals-against average in four games with the Griffins this season.
Detroit also placed forward Dallas Drake on injured reserve for a broken cheekbone sustained Oct. 18 against San Jose. He is expected to miss at least one week.