In a statement, the authorities said they wanted the monsters removed by August 6, when an annual ceremony is held on the anniversary of the 1945 bombing, BBC reported.
It follows a request by the operators of the Fukushima nuclear plant - highly radioactive after its 2011 meltdown - to keep Pokemon out of its plants.
Hiroshima's Peace Park, which includes a memorial and a museum dedicated to the 140,000 people killed in the world's first nuclear attack, occupies a large, quiet area in an otherwise crowded city.
There are around 30 Pokestops in the park, and three "gyms", where gamers can battle other players' Pokemon, reports Japanese broadcaster NHK.
Nagasaki, where 74,000 people were killed by an atom bomb days after Hiroshima, has also asked for Charizard, Pikachu and their friends to be removed from its peace park and museum.
The US Holocaust Memorial Museum also recently told visitors that playing the game there was "extremely inappropriate", while Auschwitz, where millions of people were murdered by the Nazis, has also banned the game.