The Polish team defeated Russia 19-18 in the third-place match on Sunday.
Poland's Przemysław Zamojski hit the winning shot in the last second of the match.
Serbia grabbed the gold after beating Lithuania 20-14 in the final.
Poland in July made an early exit from the Olympic tournament after losing five games and winning just two.
Russia, meanwhile, finished runners-up in the tournament in Tokyo.
3x3 basketball is a variation of the game played three a side on one basketball hoop. It made its debut as an Olympic sport at the Tokyo Games, which were held in Japan from July 23 to August 8.
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Source: PAP