"Burrows sustained an upper body injury & was taken to hospital after practice this morning for precautionary reasons. Will not play tonight," the Canucks said on their official Twitter feed.
The Flames will take a 2-1 series lead into Game 4 on Tuesday night at the Scotiabank Saddledome.
Burrows was in obvious pain after suffering the injury midway through the practice session and left the ice quickly. Reports indicate he was taken on a stretcher from the dressing room to an ambulance outside the arena.
Canucks coach Willie Desjardins said he didn't have an immediate report on the 34-year-old forward. The Canucks recalled 22-year-old forward Sven Baertschi earlier in the day.
"You guys know I won't talk about injury stuff, but he's a good player and we wanted him here in case we needed him," Desjardins said of the callup.
Baertschi was acquired from Calgary at the March 2 trade deadline in exchange for a second-round draft pick.
Burrows has two assists in three playoff games and had 33 points (18-15) in 70 regular-season games.