Draper suffered the injury during a Wednesday morning skate.
Draper, 32, has career highs with 24 goals and 40 points in 65 games. He ranks second in the NHL with five short-handed goals and is in the top 10 with a team-best plus-22 rating.
Draper is in his 13th NHL season -- his 11th with Detroit. He had played in each of the team's 229 games over the past three campaigns and had missed only seven since 2000-01.
The Red Wings began Wednesday with a league-best 85 points (37-17-9-2).