Britain were beaten semi-finalists in this year's competition, losing 3-2 to Argentina in Glasgow last week.
Leon Smith's team were bidding for back-to-back titles after ending their 79-year wait for the trophy in 2015.
The fixture on 3-5 February could feature a meeting between British world number two Andy Murray and Canada's world number six Milos Raonic.
Murray beat Raonic in this Wimbledon year's final to win his third Grand Slam title.
Britain and Canada have faced each other only once before in the Davis Cup - in Bournemouth in 1967 - as a host team comprising Mike Sangster, Roger Taylor and Bobby Wilson won 4-1.
There are 16 nations in round one of the Davis Cup World Group, with Britain seeded third.
Among the other ties, Novak Djokovic's Serbia take on Russia, while 2016 finalists Croatia will face Spain.
