Officials said they expected the death toll to rise as the Canadian province grappled with what its premier called a once-in-500-year event.
Torrential rain and mudslides have destroyed roads, cut off several mountain towns and displaced around 18,000 people.
Images show houses and vehicles in British Columbia, which sits on Canada’s west side, submerged by water after vast areas of land were flooded.
John Horgan, the province’s premier, said authorities confirmed mudslides had “claimed at least one life”.
The body of a woman has been recovered from a landslide near the small community of Lillooet. At least three others are missing.
Mr Hogan said: “We expect to confirm even more fatalities in the coming days.”
British Columbia announced a state of emergency on Tuesday night, with Mr Hogan saying this was in response to the impact of the “extreme storm”.
“This will help us secure supply chains and make sure essential goods and emergency services can reach hard-hit communities,” he tweeted.
He told residents to avoid travelling to regions under evacuation orders and alerts to allow passage for emergency workers and people delivering essential goods.
Justin Trudeau, the Canadian prime minister, said his government would help the province recover from what he called a “terrible, terrible disaster”.
Ottawa is sending hundreds of air force personnel to aid the recovery and “there are thousands more on standby,” he told reporters in Washington.
Some affected towns are in remote mountain areas with limited access and freezing temperatures.
In a press conference on Tuesday, Mr Hogan said: “The last few days have been incredibly difficult for British Columbians as we have experienced yet another natural disaster.
“Heavy rains, strong winds, flooding have devastated entire communities of our province.”
He said thousands have been forced to leave their homes under evacuation orders while “many others” have been stranded by road closures and mudslides.
The floods and mudslides have severed access to the country’s largest port in Vancouver, disrupting already strained global supply chains.
The extreme flooding in British Columbia comes just months after wildfires ravaged the province.
Additional reporting by agencies
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