World number five Tsitsipas lost 7-6(7), 7-5 to Chilean Nicolas Jarry, ranked 28 in the world.
It marks the third consecutive time the Greek has been knocked out in the second round of the Wimbledon warm-up tournament.
In Wednesday's late match, home favourite Alexander Zverev defeated Canadian Denis Shapovalov in straight sets, 6-2, 6-4.
Zverev, the 26-year-old Olympic gold medallist, made the finals at Halle in 2016 and 2017 but lost to Roger Federer on both occasions. He will next face Jarry.
Earlier on Wednesday, Medvedev defeated Serbian Laslo Djere 6-3, 6-7(5), 6-3, with the world number three overcoming losing a tight second set to win with ease.
"Grass is so tough for me," said Medvedev. "You can actually play a perfect match and lose on two tie-breaks, so it's a little bit strange for me.
"When I see top players like Roger Federer, from one side they can seem like aliens but you try to see the best in them, and how they are able on this surface, where it's sometimes tricky to beat anyone, to have so many titles. Wimbledon, Halle, whatever.
"It's just amazing and that's what I try to watch. Happy to win and looking forward to the next matches."
The former world number one and 2021 US Open champion was runner-up on the Halle grass in 2022, losing to Hubert Hurkacz in straight sets in the final.
Medvedev has struggled on grass in his career so far and has never reached the quarter-finals at Wimbledon.
He will next face Spanish eighth seed Roberto Bautista Agut.
He missed last year's tournament at the All England Club due to Wimbledon's ban on Russian and Belarusian players competing.
Medvedev has won five ATP titles already this year, but was beaten by Sebastian Korda in the Australian Open third round and was dumped out in the French Open first round for the fifth time in seven appearances.
