Norrie, 28, conceded two early breaks in the opening set against Medvedev and left himself with too much to do.
He was blown away by Medvedev’s serve in the second set, with the Russian winning eight of nine first-serve points.
The world number three was happy to progress, but expressed concerns about the balls being used after the win.
“It’s a bit strange,” said Medvedev. “The court is pretty fast but the balls get old very fast.
“So at one moment in the rally, you feel like there isn’t much you can do, so you can’t go for the winner because the risk-reward isn’t there.
“It’s the same for the opponent, so we just hit, hit.”
Meanwhile, Australian Open winner Jannik Sinner lost the first set to the Netherlands’ Tallon Griekspoor before the Italian recovered after a rain break to win 5-7 7-5 6-1.
Norway’s seventh seed Casper Ruud progressed with a 6-3 6-4 victory over Spain’s Alejandro Davidovich Fokina.
However, Denmark’s Holger Rune suffered a 6-1 6-1 defeat by Hungary’s Fabian Marozsan in 59 minutes.