The 26-year-old was taken to hospital and tests confirmed he does not have a concussion.
"He's doing well enough this morning so that's good news," Canadiens coach Dominique Ducharme said Wednesday. "Tests have been done and there was nothing positive, like he doesn't have a concussion, at least for now. So it's really day to day. He'll be re-evaluated over the next 24 hours and we'll see tomorrow."
Drouin waved his arm but was unable to avoid being struck by teammate Brett Kulak's rising wrist shot in the first period against the Red Wings at Bell Centre. Drouin grabbed his head, immediately skated off the ice and was escorted to the locker room with 12:20 remaining.
"You know, at first I didn't really see what happened," Canadiens forward Josh Anderson said. "Obviously, I knew that he got hit in the head, but I didn't know where, so I went to go check on him in the first period but he was off to the hospital getting checked on. And then I just saw him after the game. Everything went well. Obviously he's going to get looked at again tomorrow, but he just went there for precautionary reasons, but it looks like he's OK. But anytime you see that, it's very scary."
Drouin, who moved from wing to center Tuesday, is second on the Canadiens with seven points (two goals, five assists) in 11 games, behind forward Nick Suzuki (eight points; one goal, seven assists).
Last season, Drouin left the Canadiens on April 28 because of issues brought on by anxiety and was placed on long-term injured reserve.