Medvedev broke Murray's serve in the third game of the first set and never looked back as he completed a comfortable 6-4 6-2 victory at the Hard Rock Stadium.
The Russian was in cruise control for most of the match. He didn't have to face a break opportunity once and secured the win on his first match-point chance as the Scot hit a backhand return into the net.
Despite the early exit, Murray, who was playing under the watchful eye of Ivan Lendl remains positive that his game will improve.
"My level of tennis is obviously not right now where it needs to be to win matches like that," Murray said at his post-match press conference.
"I think today there was some good signs on the court, but the two sort of key things in tennis is serve and return, and I didn't do either of them particularly well."
On his renewed partnership with Lendl, which first began at the start of the 2012 season, Murray said: "I think probably (he will bring) some clarity over the right way to play and the right way to practice.
"I don't feel I have been practicing the right things probably for 18 months or so and it is difficult to sort of undo that in the space of a few weeks obviously.
"Hence (that is) one of the reasons why I am taking a big period of training to try and change some of those things and hopefully get my game into a place where it's more competitive against the top players again."
The former world number one, who has battled back to fitness from hip problems, is set to skip the clay season so his focus can be solely on preparing for the grass-court tournaments.
"As players are maybe getting older maybe (they are) prioritising specific like parts of the season where maybe they can feel they can be more successful," he said.
"For me the last two years I had the problem in Miami last year and then tried to play on the clay and aggravated the problem, then I was very close to missing the grass season.
"It was just more a decision that me and my team took because I feel like my chances of doing well on the grass are higher.
"It was maybe the right decision to skip it, then I do also need a period of working on my game and improving some things and try and get some better habits ingrained."
Meanwhile, Miomir Kecmanovic upset world number seven Felix Auger-Aliassime as he coasted to a 6-4 6-2 victory.
Defending champion Hubert Hurkacz hit 17 aces in his 7-6 (5) 6-2 win over Frenchman Arthur Rinderknech.
American 11th seed Taylor Fritz needed three sets to beat qualifier Mikhail Kukushkin 6-3 5-7 6-3 and reach the third round.
The other men's seeds beaten in their second-round matches on Saturday included Denis Shapovalov, Nikoloz Basilashvili, Karen Khachanov, Daniel Evans, Christian Garin and Albert Ramos-Vinolas. Sebastian Korda of the US saved a match point on the way to topping Ramos-Vinolas 4-6 7-6 (6) 6-3.
Tommy Paul of the US got the upset over Khachanov, winning 6-4, 3-6, 7-6 (3). Paul improved to 14-7 on the year and will next meet world number 11 Taylor Fritz, the highest-ranked American.
Another American, Jenson Brooksby, had the upset over Basilashvili 6-3 6-1.
Other seeded men's winners included Stefanos Tsitsipas, Carlos Alcaraz, Roberto Bautista Agut, Marin Cilic, Alex De Minaur and Aslan Karatsev.
Elsewhere, there was disappointment for Britain's Heather Watson in the WTA event as she was beaten in straight sets by Belinda Bencic.
Watson, who recently dropped out of the top 100, had defeated 20th-ranked Elina Svitolina in the last round.
However, the Swiss world number 28 proved too strong as Bencic progressed 6-4 6-1.
Former world number one Naomi Osaka was handed a walkover into the fourth round after Karolina Muchova withdrew because of an abdominal injury.
Ninth seed Danielle Collins, the Australian Open finalist, won 6-1 6-4 against Russian Vera Zvonareva, who wore a visor with the message "No War" written on the side.
And No. 8 Ons Jabeur also got an easy win, topping Kaia Kanepi 6-3, 6-0.