The US Holocaust Memorial Museum has asked people not to play Pokemon Go on their phones during their visit.
A spokesman for the museum in Washington said that playing the game inside a memorial to victims of Nazism was "extremely inappropriate".
The Arlington National Cemetery, just three miles away from the museum, has also warned off Pokemon players.
Both locations feature in the new smartphone game, which has become a commercial and cultural phenomenon.
Pokemon Go allows players to search locations in the real world to find Pokemon creatures.
It topped the app store download chart on both iPhone's App Store and Google Play just days after its release in the US, Australia and New Zealand.
Like many other landmarks, both the museum in Washington and the military cemetery in Virginia are places where players can come across Pokemon creatures.
They are both reportedly also Pokestops, where players can collect virtual items like snacks and medicine for Pokemon, but officials at the museum are trying to get it removed from the game.
And the cemetery has also made its move to address the new craze.
"Playing games such as Pokemon Go on these hallowed grounds would not be deemed appropriate," cemetery officials said in a statement.
Spokesman Stephen Smith said they had not experienced any problems yet but wanted to act before they potentially arose.
It would be hard to know whether someone was playing the game on their phone or using the cemetery's own app to find their way round.
There has been no response yet from game developers Niantic Labs on whether it could stop Pokemon creatures from appearing inside the Holocaust Museum.