The world No.4 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 Olympic 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 No.44-ranked Serbian opponent.
Krajinovic said: "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."
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.
The No.2 seed Pablo Carreno Busta, from Spain, prevented a third Serbian reaching the final four, beating Dusan Lajovic 7-6 (7-4) 6-3, and he will face Federico Delbonis on Sunday (AEST).