"The doctors want no blood on his eye before he plays," Red Wings general manager Ken Holland said Wednesday.
"It's a blow because he scored 30 goals this season, and he's one of our key players. But we expect to get him back at some point in the series, and that's good news for us and him."
Defenceman Brett Lebda also will miss Game 1 with a sore ankle and concussion.
Calgary's Craig Conroy hit Holmstrom with his stick at 6:44 of overtime Sunday night in Detroit's series-winning victory over the Flames. The 34-year-old left-winger had 30 goals and 22 assists during the regular season.
Lebda, 25, hasn't played since Saturday when he twisted awkwardly into the boards while checking Daymond Langkow. He was called for tripping, and Langkow punched him in the face while both were on the ground. Lebda played in 74 games for Detroit during the season, adding five goals, 13 assists and solid defence.