The Serbian defeated Medvedev 6-3 6-4 in the Giorgio Armani Tennis Classic at The Hurlingham Club.
The 29-year-old from Nottingham had reached the quarter-finals at Queen’s last week.
Novak Djokovic proclaimed himself "pain free" after defeating Daniil Medvedev in an exhibition match on Friday ahead of Wimbledon. I was pain-free and I'm really glad.