One Twitter user wrote: "What has happened to the world?"
And one outraged social media user said: "I honestly am wondering if we're on the verge of a global breakdown."
The game has benefited Nintendo - shooting its value up by 36 per cent in just two days.
The video game company's shares rose 25 per cent on Monday as recorded the biggest one-day gain for more than 30 years after Pokémon Go - only the company's second foray into smartphone gaming - was downloaded by million of users in a matter of days.
The augmented reality app uses a smartphone's camera to superimpose animated Pokémon creatures onto the real world, and encourages players to walk around a neighbourhood to catch different virtual creatures.
The game is free, but players can pay for additional items to give them an edge, leading investors to speculate that Nintendo can cash in on the same wave that has proved lucrative for companies such as Finland's Supercell, the maker of Clash of Clans.