The Russian won with a score of 7:5, 7:5.
Medvedev made four aces, made five double faults and realized three break points out of 13. The Canadian realized one break point out of four, made five double faults and made two aces.
Medvedev's next opponent will be American Taylor Fritz.
The match will take place on August 19.
Earlier it was reported that the Russian Andrei Rublev could not defeat Fritz in the second round of the Masters series tournament in Cincinnati.