The 27-year-old tennis player from Russia defeated Briton Liam Broedy in two sets with a score of 6:4, 6:3 in the second round match.
The game lasted 1 hour 33 minutes.
Medvedev's next opponent (third seed) will be Christopher O'Connell of Australia.
The prize fund of the tournament in Doha is more than $1.3 million.
Earlier it was reported that Lyudmila Samsonova could not get into the 1/4 finals of the WTA tournament in Dubai (UAE).