The Spaniard's withdrawal means Medvedev will be top seed at the March 1-7 event, which also features top-10 players Stefanos Tsitsipas and Alexander Zverev.
'The players and all of the fans need to try to give it a chance to see how it goes and I think we'll have a better idea after the tournament is finished.'
Murray, who suffered an elbow injury in March and made his return from a five-week layoff on Wednesday after a first-round bye, won the opening set in 48 minutes before losing concentration.
Novak Djokovic sauntered past Spaniard Feliciano Lopez to reach the quarter-finals of the Shanghai Masters on Thursday but Andy Murray had to claw past big-serving American John Isner after losing a first-set tiebreaker.
A round-up of results from Davis Cup matches played on and Sunday
Andy Murray took a step closer to a first title in arguably the toughest year of his playing career, grinding out a 3-6, 7-5 ,6-2 win over Ugo Humbert on Saturday to reach the final of the European Open in Antwerp.
Bulgaria's Grigor Dimitrov upset top seed and defending champion Milos Raonic of Canada at the Brisbane International on Saturday to set up a title clash against Japan's Kei Nishikori.
ormer world number one Andy Murray showed some more positive signs in his injury comeback but eventually went down in a bruising battle with Italy's Fabio Fognini.
There is not much that spooks Rafael Nadal at the French Open but David Ferrer managed to do just that - for 49 bewitching minutes - before watching in despair as his fellow Spaniard turned into a man possessed to set up a semi-final with Andy Murray.
Defending champion Novak Djokovic survived a scare.
Novak Djokovic gave a brutally honest assessment of his performance after losing the Wimbledon final 6-4, 7-5, 6-4 to Andy Murray on Sunday.
Carlos Alcaraz beat Novak Djokovic in the Wimbledon final to win his fourth Grand Slam title.
World No 1 Novak Djokovic and defending champion Andy Murray produced contrasting performances to secure their berths in the quarter-finals of the Madrid Masters on Thursday.
Briton Andy Murray will return from injury at the Legg Mason Tennis Classic in Washington at the end of July after being given the all-clear by his doctor.
Former U.S. Open champion Samantha Stosur has turned to Andy Murray's former coach Miles Maclagan to help reverse her slide down the world rankings, Tennis Australia said on Thursday.
?Andy Murray's preparations for this month's Australian Open suffered a setback on Wednesday when the world number two went down in straight sets to local favourite Nick Kyrgios at the Hopman Cup in Perth.
Olympic and Wimbledon champion Andy Murray picked up where he left off in Rio by drubbing Argentina's Juan Monaco to take his place in the third round of the Western & Southern Open in Cincinnati on Wednesday.
'Of course I am happy to reach No. 1. It was my goal since I was young and especially my goal in the latest times.'
A lot has happened to Andy Murray in the three years since he choked back the tears on Centre Court after a four-set defeat that handed Roger Federer the Wimbledon trophy for a seventh time.
A round-up of Friday's action in the Davis Cup.
It may have been the Labor Day holiday in the United States on Monday but Andy Murray came ready to work, demolishing Grigor Dimitrov 6-1, 6-2, 6-2 to storm into the quarter-finals of the US Open.
Wimbledon champion Andy Murray, the first British winner of the men's title for 77 years, was named BBC Sports Personality of the Year on Sunday.
With reports suggesting that Andy Murray, who finished the ATP year as world No 1 player, might be in line for a knighthood, the Briton has insisted that he is "too young" for the country's "highest honour." The 29-year-old, who beat Novak Djokovic in the ATP World Tour Finals on Sunday, has been tipped to be named in the New Year honours list.
Fourth seed Andy Murray erased memories of early losses at Indian Wells by storming into the BNP Paribas Open third round with a ruthless 6-1, 6-3 victory over Canadian Vasek Pospisil on Saturday.
Davis Cup champions Britain were locked at 1-1 with Japan after the opening two singles of their World Group, first-round tie on Friday after Andy Murray gave the hosts the lead.
Andy Murray underlined his hunger for more Grand Slam silverware on Sunday when he said he would pass up the chance to be world number one if it meant he could taste more major success.
Brothers Andy and Jamie Murray carried Britain to the brink of a Davis Cup semi-final berth after they beat France in the doubles rubber to take a 2-1 lead ahead of Sunday's reverse singles.
Federer has been brandishing an aggressive style of play, forcing the action and rushing in to half-volley weak second serves to forge an advantage.
Swiss seventh seed Belinda Bencic was stunned by Slovakia's Magdalena Rybarikova while former champion Ana Ivanovic was also sent packing in third-round action at the BNP Paribas Open in California.
Former world number one Andy Murray won his first ATP tour singles match in nearly nine months with a 6-3, 6-7(6), 6-1 victory over American Tennys Sandgren in the opening round of the Zhuhai Championships.
India's Somdev Devvarman was beaten in straight sets by World No. 11 Andy Murray in the second round of the ATP Shenzen Open, in Shenzhen, on Thursday.
'There are a number of unique challenges elite tennis players have to face. The game is gladiatorial in nature with nowhere for players to hide and no team mate or manager to help deflect the pressure.'
Photos from the matches played at the Miami Open on Monday
The tournament will be Murray's third since hip surgery in January and mark his return to the hard courts for the first time since March 2017 at Indian Wells.
Following Rafael Nadal's problems with cramps in the second round of the Australian Open on Wednesday, Andy Murray has taken a swipe at critics who gave him a hard time after his own struggles at the US Open.
When it comes to the Australian Open the Serbian reigns supreme.
World No 2 Andy Murray overwhelmed Italy's Andreas Seppi 6-2, 7-5 and second seed Rafael Nadal crushed veteran Italian Paolo Lorenzi 6-1, 6-1 to reach the China Open second round on Tuesday.
Certainly the prospect of another showdown at the US Open in a few weeks is exciting, but whether or not 23-time Grand Slam champion Djokovic can stretch his career long enough to battle Carlos Alcaraz on a regular basis is questionable.
With British hopes of elusive home success once again resting on his shoulders, Andy Murray could have been forgiven an envious glance Novak Djokovic's way after the Wimbledon draw was made on Friday.
Andy Murray took another step towards securing a berth at next month's World Tour finals when he fought off a typically dogged David Ferrer to win 6-4, 7-5 and move into the final of the Valencia Open on Saturday.
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