Murray,who won his first game since September in beating Australian James Duckworth in the first round,put up a competitive first set against Medvedev in which he responded to being broken in the third game by breaking back five games later.
But the resistance would not last much longer as the Russian took another break at 5-5.
The second set was more one-sided,with Medvedev not looking back from a 4-0 lead before wrapping up the match in an hour and 23 minutes.
"If you're not serving as well,or if you're not moving as well,the better players exploit that,"Murray said.
"He is a top player and is able to do that.
"So I need to try and find a way of working out how to get around some of the things I struggle with a little bit now,and I'll try to do that."