Medvedev, ranked No 5, led 5-3 when Dimitrov, ranked No 10, pulled out on Sunday evening at the All England Lawn Tennis and Croquet Club in London.
The Russian will play Italian Jannik Sinner, the top seed, next.
Earlier in the tournament, Daniil Medvedev won against American Aleksandar Kovacevic (6-3, 6-4, 6-2), Frenchman Alexandre Muller (6-7 (3), 7-6 (4), 6-4, 7-5) and German Jan-Lennard Struff (6-1, 6-3, 4-6, 7-6 (3)).
The 33-year-old Bulgarian defeated Serb Dusan Lajovic (6-3, 6-4, 7-5), Chinese Juncheng Shang (5-7, 6-7 (4), 6-4, 6-2, 6-4) and Frenchman Gael Monfils (6-3, 6-4, 6-3) in the previous rounds of The Championships.
London (Grand Slam), other last 16 results (All England Lawn Tennis and Croquet Club, grass, GBP 50.000.000, most recent results first):
- Holger Rune vs. Novak Djokovic
- Taylor Fritz vs. Alexander Zverev
- Arthur Fils vs. Alex De Minaur
- Lorenzo Musetti vs. Giovanni Mpetshi Perricard
- Tommy Paul vs. Roberto Bautista Agut: sunday
- Jannik Sinner beat Ben Shelton (14): 6-2, 6-4, 7-6 (9)
- Carlos Alcaraz (3) beat Ugo Humbert (16): 6-3, 6-4, 1-6, 7-5