He will next face eighth-seeded Spaniard Roberto Bautista Agut.
He missed last year’s tournament at the All England Club due to a ban on Russians and Belarusians competing at Wimbledon.
Medvedev has won five ATP titles this year, but was beaten by Sebastian Korda in the third round of the Australian Open and eliminated in the first round of the French Open for the fifth time in seven appearances.