The fight broke out between a motorist and a pedestrian on Sunday at the carpark entrance of a mall in Singapore's popular Orchard Road shopping district.
According to a police statement, the pedestrian was playing the augmented reality game on his phone while crossing the road.
The motorist honked his horn at the player, setting off an argument which led to the fight.
Both men were arrested for affray, an offence which carries a jail term of up to a year, a Sg USD 5,000 fine or both.
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Pokemon Go enables users hunt fictional digitised animal characters like the furry yellow Pikachu, which have been scattered around the world, often in unlikely locations.
The game has become a global craze, with crowds of players dashing to locations to try to snag characters.
In the ten days since it launched in Singapore, the police have issued safety warnings urging pedestrians to be aware of their surroundings and watch out for traffic while playing.
Pictures on local social media show hundreds gathered in Hougang, a suburb popular for catching rare Pokemon characters.
Authorities worldwide are grappling with the explosive popularity of the gaming app, which has caused accidents and prompted bans.