The 23-year-old Russian reached the last four at Queen's Club for the first time after a comprehensive 6-2 6-2 victory lasting just an hour and 16 minutes.
Schwartzman had knocked out defending champion Marin Cilic in the second round, in only his third career win on grass, but Medvedev proved too strong for the Argentinian.
Felix Auger-Aliassime became the youngest Queen's semi-finalist since Lleyton Hewitt in 1999 when he shocked top seed Stefanos Tsitsipas.
The 18-year-old Canadian had played two full matches on Thursday, including a taxing three-setter against Nick Kyrgios.
But he showed no ill-effects, with a run of five games in a row at the end of the first set and the beginning of the second proving the difference in a 7-5 6-2 victory.
Auger-Aliassime has beaten Tsitsipas in all five of their matches, stretching back to their time as juniors.
"Yeah, it's true that I have happened to play well every time we've played," he said. "We've had tough encounters in juniors, three sets, tight two sets.
"I think this year, both times I served really well, played really well, played pretty aggressively. But at the same time, I feel like all these matches have different stories, different background, different surfaces.
"But, yeah, it's good to have this record, and hopefully I can keep it."
Medvedev, the first Russian semi-finalist at Queen's in the Open era, will face Gilles Simon.
World number 38 Simon won a tight all-French clash against Nicolas Mahut 7-6 (5) 5-7 7-6 (3).
Feliciano Lopez booked the final last-four spot with victory over sixth seed Milos Raonic.
Andy Murray's Spanish doubles partner dropped the first set but hit back to win 4-6 6-4 7-6 (5).
Lopez, the winner at Queen's in 2017 who was handed a wild card this year, will meet Auger-Aliassime in Saturday's semi-final.
