The museum drew heavy criticism for agreeing to host a ceremony at which Mr Bolsonaro, who has advocated relaxing environmental policies, was scheduled to receive a person of the year award.
Museum officials said the event would now be held at a different location.They said that the museum in New York was "not the optimal location".
How did this row erupt?
The Brazilian-American Chamber of Commerce, a non-profit non-governmental organisation that promotes trade, investment and cultural ties between the two countries, hired the museum's Hall of Ocean Life for its annual gala to be held on 14 May.
At the annual event, the chamber gives out its person of the year awards. This year one of those prizes is going to Mr Bolsonaro, who was sworn in as Brazil's president on 1 January.
On its website, the organisation said it had chosen the far-right leader in recognition of "his strongly stated intention of fostering closer commercial and diplomatic ties between Brazil and the United States and his firm commitment to building a strong and durable partnership between the two nations".
Previous recipients of the award have included former US President Bill Clinton and former New York Mayor Michael Bloomberg.What were the objections?
Climate activists and environmental organisations such as Greenpeace have denounced Mr Bolsonaro as "a threat to Brazil's ecosystem".
Most of those opposed to having the museum host the event pointed to the president's plans to open up parts of the Amazon rainforest for development, which they argued was not in keeping with the museum's mission.
In a radio interview on 8 April, President Bolsonaro said he wanted the US to join in a development plan for the Amazon region. He also said that demarcations of indigenous reserves hampered development of the region and that he would abolish them if he could find a way to legally do so.
New York Mayor Bill de Blasio said President Bolsonaro was a "very dangerous human being".
Mr de Blasio told radio station WNYC. "He's dangerous not just because of his overt racism and homophobia, but because he is unfortunately the person with the most ability to be able to impact what happens in the Amazon going forward."
Scientists with ties to the museum threatened to resign if the event went ahead and many made their anger public on social media.
What did the museum say?
When the controversy first broke last week, the museum tweeted that its hall had been booked "before the honouree was secured".
A day later, and after almost 3,000 people had commented on the tweet, most of them expressing their concern over President Bolsonaro's environmental policies, the museum tweeted again, thanking people for their thoughts.
On Monday, the museum announced its decision to cancel its hosting of the event.
It is not yet clear where it will be held. President Bolsonaro has not yet reacted to the change of venue.