The US Open champion and world number two fired four aces in the first set and broke in the third game as Murray, who underwent hip surgery three years ago, limped slightly across the court.
Murray, who scored his 700th career win at Indian Wells two weeks ago, saved two break points in the fifth game of the second set but Medvedev seized his third when the Briton sent a kick out of the backline.
The Russian player broke his opponent’s serve once more in the seventh game, following losing only two of the first service points in the set and deciding the victory in less than 90 minutes.
Medvedev is three wins away from returning to the top of the men’s singles world rankings following losing the lead following his surprise loss in the third round of the Indian Wells Championships to Frenchman Gael Monfils.