As many as 290 such incidents were recorded across England and Wales throughout July, soon after the game was launched in the UK.
Lancashire Constabulary logged 39 incidents, marking the highest figure from 29 police forces across the UK that provided data to BBC under the UK's Freedom of Information Act.
"It was out in America first and there seemed to have been a few problems there. Nationally and internationally I'm well aware of quite a few circumstances that have come up.
Scotland Yard and Greater Manchester Police said they had noted incidents of Pokemon "lures" being set up, as robbers used the game to distract victims before snatching their mobile phones.
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British Transport Police recorded two incidents of children trespassing on railways while playing the game.
Niantic, the firm behind the popular gaming app, said the company takes the issue of "player safety" seriously.
"We encourage all people to be aware of their surroundings and to play alongside friends or family, especially when you're exploring unfamiliar places. Please remember to be safe and alert at all times, don't drive and play, abide by local laws and respect the locations you visit," a spokesperson said.