The world number four made a fast start to his match against Filip Krajinovic, winning the opening five games, but fell away to lose in three sets after an hour and 59 minutes.
Tsitsipas is due to represent Greece at the behind-closed-doors Games in Japan, where he will be among the medal favourites.
His racket bizarrely fell apart in the second set against Krajinovic, with Tsitsipas left clutching just the handle as the head broke off when he attempted a backhand.
Despite reaching for a replacement racket, Tsitsipas could not get the better of his 44th-ranked Serbian opponent.
Krajinovic said, according to the ATP website: “He started really well, really aggressively. I could not find my game, could not find my serve, he was overpowering me. But at the end of the first set, I started to feel better, I was going for my shots.
“It paid off in the end. I am happy to beat Tsitsipas, he is an amazing player. I always play well here, and I hope I keep playing well here.”
What just happened
A *unique* racket malfunction from @steftsitsipas in Hamburg… pic.twitter.com/YhpcJp1qLS
— Tennis TV (@TennisTV) July 16, 2021
Krajinovic advances to take on a fellow Serbian, Laslo Djere, in the semi-finals, after Djere swept to a 6-2 6-2 win over Georgian Nikoloz Basilashvili.
Spanish second seed Pablo Carreno Busta prevented a third Serbian reaching the final four, beating Dusan Lajovic 7-6 (7-4) 6-3, and he will face Federico Delbonis on Saturday.
At the Nordea Open in Bastad, Sweden, top seed Casper Ruud had his path to the semi-finals smoothed by the withdrawal of scheduled opponent Henri Laaksonen due to injury.
That walkover means Norwegian Ruud will next tackle Roberto Carballes Baena, who beat Slovakian Norbert Gombos 6-4 6-2.
Chilean second seed Cristian Garin bowed out, beaten 6-4 4-6 6-2 by Argentinian Federico Coria. Coria’s semi-final opponent will be Germany’s Yannick Hanfmann, a 6-4 6-3 victor over French qualifier Arthur Rinderknech.
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