The 50-year-old from West Dunbartonshire had been white water rafting on the Kettle River, near Grand Forks, British Columbia, on Saturday.
He was on holiday at the time with his wife Carol and 16-year-old son Andrew.
The bodies of two elderly local people, who were swept away with Mr Barrie, have been recovered.
A statement from the UK Foreign Office, on behalf of Mr Barrie’s family, said: “It is with great sadness and grief that we can confirm that Andrew Barrie, age 50, of Balloch, Alexandria, Scotland, is missing presumed drowned.
“He was on holiday in Canada with his wife Carol and 16-year-old son Andrew.
“What had started as a beautiful, peaceful float on the river, with friends who knew the river well, turned to tragedy with the loss of three lives.”
The statement said two bodies recovered were those of local people who had lived in the area for 10 years.
It is understood that they were Ronald Legare, 74, and 71-year-old Jean Legare.
The couple, from Lake Christina, were thought to be part of a group of 13, including Mr Barrie which was tubing and rafting.
Witnesses spoke of seeing three people being swept over the waterfall after their crafts capsized.
The statement concluded: “The river is normally calm and was used by other people on the same day.
“However, due to recent heavy rain one particular stretch of the river was treacherous with strong currents.
“There are no signs anywhere indicating the possible dangers and we had no concerns whatsoever on being on the water that day. Rescue teams continue to search for the body.”