Zverev has now won 15 sets in a row after recovering from two sets down against qualifier Oscar Otte in the first round.
He easily brushed aside the 46th-ranked Davidovich who hit 37 unforced errors and only 16 winners in his first major quarter-final.
"It's nice to be in the semi-finals, but just being here doesn't satisfy me," said Zverev, the 2020 US Open runner-up.
Tsitsipas hopes to stay on course for a first Grand Slam final when he meets Medvedev under the lights on Court Philippe Chatrier, the last match to be played behind closed doors before the easing of a nationwide curfew.
The Greek fifth seed will try to reach a third successive major semi-final, having lost a thrilling five-setter to Novak Djokovic in Paris last year.
Blocking his path is second seed Medvedev, the Russian who hadn't won a match in four previous visits to the French Open but has looked increasingly assured on clay over the past week.
Medvedev, a runner-up at the 2019 US Open and this year's Australian Open finalist, holds a 6-1 head-to-head advantage over Tsitsipas.
He beat the Greek in straight sets in the last four in Melbourne in their most recent meeting.
"I feel like I don't have to think against who I'm facing or not, I just have to play my game, let the rest be witnessed," said Tsitsipas.
Medvedev could take over the number one ranking if he reaches the final and Djokovic does not.
He has a career win-loss record of 15-20 on clay, but the return of Roland Garros to its traditional May-June slot and far warmer temperatures have helped the Russian shake off bad memories of past editions.
"Definitely a better feeling than losing the first round, going home on Tuesday like I think two or three times I lost here Sunday. It's not a good feeling. I hope it's going to be better with every year," said Medvedev.
Roland Garros Alexander Zverev