The 60-year-old woman, whose name wasn't released, was attacked Sunday afternoon on Cow Bay on Flores Island, a remote island off the coast of Vancouver Island in British Columbia, police said.
She was airlifted to a hospital in Victoria where her condition was upgraded from critical to stable Monday, the Canadian Broadcasting Corp. reported.
Sgt. Ben York of the provincial Conservation Service said the cougar was found dead Monday morning by a team assisted an experienced cougar hunter with tracking hounds, the CBC said.
Capt. Ray Jacobson of the Joint Rescue Coordination Center, based in Victoria, said the couple, who apparently live on the island, had previous encounters with the big cat.
"They've seen it for about a month now, they've had run-ins with it," Jacobson said.
"When she was attacked, her husband was able to basically fend the cougar off."
He said the husband injured the cougar and it ran off into the bush.
The same woman had an encounter with a cougar two months ago, but conservation officials were unable to track or capture the animal, the CBC said.