Murray began the defense of his title with a straight-set win over Kazakhstan's Alexander Bublik on Centre Court, BBC reported.
The Scot won 6-1, 6-4, 6-2, despite a hip injury which disrupted his buildup.
The 30-year-old will face Germany's Dustin Brown - the man who beat Rafael Nadal in 2015 - in round two.
"With the adrenaline, it helps numb some pain that you might have and I moved well," Murray told BBC Sport.
"I thought I did pretty well for the first match."
"In the first few days, normally the court is a bit lush and can be a bit slippy, but I didn't feel like I was losing my footing at all."
Spanish world number two Nadal beat John Millman 6-1, 6-3, 6-2.
He will next face American world number 43 Donald Young, who was 2-1 up in sets when opponent Denis Istomin retired.
Nadal missed last year's Wimbledon because of injury and was playing his first tournament match on grass in two years.
He is looking to secure a second Gram Slam title in 2017 after winning last month's French Open.
"I have been playing good tennis since the beginning of the season," said Nadal.
"The clay-court season has been special and emotional and here I have an opportunity to perform on grass."
Three-time Grand Slam champion, Wawrinka, needed ice on a knee injury between points as he fell to a 6-4, 3-6, 6-4, 6-1 loss on Centre Court.
Medvedev's victory over world number three came just hours after the 21-year-old moved into the world's top 50 for the first time.
It was his first Grand Slam victory on his Wimbledon debut, and he celebrated by dropping to the court in front of the net and kissing the ground.
"At 5-1, I started thinking about what to do after the match and I kissed the grass because it was my first Grand Slam win, even though people do it when they win Wimbledon," he said.
"One year ago I was 250th in the rankings and if someone said I would not only play on Centre but win I would say: 'You are joking! "