With Medvedev ahead 5-3 in the first set on Court One, Bulgarian 10th seed Dimitrov opted to retire as he struggled to move freely.
Dimitrov had suffered what looked like a knee injury when he slipped after racing into a 3-0 lead. He took a medical timeout before unsuccessfully trying to carry on playing.
Former US Open champion Medvedev will face world number one Jannik Sinner for a place in the semi-finals.
The 28-year-old reached the semi-finals last year in his best run at the All England Club before losing to eventual champion Carlos Alcaraz.
Medvedev will be aiming to avenge his Australian Open final loss to Sinner earlier this year when he plays in the top seeded Italian in the last eight.