Murray won the Canadian Open in 2009, 2010 and 2015Andy Murray lost in straight sets in the first round of the Canadian Open but fellow Briton Cameron Norrie progressed at the tournament in Montreal.
Three-time champion Murray was beaten 6-1 6-3 by American Taylor Fritz.
British number one Norrie, who lost in the final of the Los Cabos Open to Daniil Medvedev on Sunday, beat American Brandon Nakashima 6-4 6-4.
There were also wins for Britain's Jack Draper and Dan Evans.
After a 24-hour delay because of rain, Fritz - world number 13 and a quarter-finalist at Wimbledon last month - produced a dominant performance that several times reduced Murray to smashing his racquet against the court in frustration.
It took Norrie just took just 73 minutes to beat Nakashima. The world number 11 will face Botic van de Zandschulp in the second round.
Draper set up a meeting with Greece's world number five Stefanos Tsitsipas after beating France's Hugo Gaston 6-2 6-3.
Evans defeated Filip Krajinovic of Serbia 6-2 1-6 6-0 either side of a rain delay and will now play Russia's Andrey Rublev, who had a bye in the first round.
Nick Kyrgios, who claimed his first ATP Tour title since 2019 at the Citi Open on Monday, is through to the second round after a 6-4 6-4 win over Argentina's Sebastian Baez.
The Australian, ranked 37th in the world, will face world number one Medvedev in the second round.
In the women's event in Toronto, British number one Emma Raducanu lost in straight sets to the Italian defending champion Camila Giorgi.
