The 27-year-old left wing sustained the injury blocking a shot by Ryan Graves at 4:15 of the second period of a 5-2 win at the New Jersey Devils on Saturday.
With Bertuzzi and forward Jakub Vrana (personal reasons) sidelined for the 5-4 overtime loss to the Los Angeles Kings on Monday, forward Filip Zadina made his season debut. Zadina had no shots on goal, one hit and one blocked shot in 14:25 of ice time after being scratched the first two games of the season.
"It's an opportunity and I'll try to do my best," Zadina said beforehand. "I'll go and prove I am a good player."
Zadina had 24 points (10 goals, 14 assists) in 74 games last season.
Bertuzzi has one assist and four shots on goal while averaging 13:38 in ice time in two games this season.
Last season he was second on the Red Wings in goals (30) and points (62) in 68 games.
The Red Wings also are missing forward Robby Fabbri (knee).
"Obviously, it's a tough loss with Fabbri also out, two top-six guys, arguably two first-line guys," coach Derek Lalonde said. "But that is why you have the depth. [General manager] Steve [Yzerman] had a very good offseason and he wanted to have some depth. I like our lineup despite who is out, and that is a credit to having some more depth than Detroit has had the luxury of in the past."
Among the Red Wings' offseason moves were the signings of forwards Andrew Copp (five-year contract), David Perron (two-year contract) and Dominik Kubalik (two-year contract). Copp has two assists in three games, Perron scored the game-winning goal against the Devils and had three points (two goals, one assist) Monday, and Kubalik also scored against New Jersey before getting two assists against Los Angeles.
NHL.com independent correspondent Dave Hogg contributed to this report