Bolsonaro, who has been attacked at home and abroad for policies that critics say threaten the environment and indigenous communities, is due to receive an award at the museum from the Brazilian-United States Chamber of Commerce.
"The external, private event at which the current President of Brazil is to be honored was booked at the Museum before the honoree was secured," the museum tweeted on Thursday.
"We are deeply concerned, and we are exploring our options."
Bolsonaro was chosen to receive the "Person of the Year" award from the chamber at a May 14 gala dinner attended by more than a thousand people.
The website Gothamist quoted one environmentalist as saying it was "a particularly bitter irony ... that a man intent on destroying one of the world's most prized natural resources would be anointed Person of the Year inside a space dedicated to the celebration of the natural world".
In an open letter published in the French newspaper Le Monde on Wednesday, 13 representatives of Brazilian indigenous peoples denounced Bolsonaro's environmental policies, saying they left them on the verge of "an apocalypse".
"The government wants to monopolize the entire Amazon, bleed it even more by building new routes and railroads," it said.
Since taking office on January 1, Bolsonaro has rolled back environmental protection laws in favour of miners and farmers.