"Our show simply cannot, in good conscience, participate and be a part of this new culture that is being imposed on the Kennedy Center," producer Jeffrey Seller said in a statement on Wednesday.
Lin-Manuel Miranda's hip-hop-flavoured biography about the first US treasury secretary, Alexander Hamilton, won the best new musical Tony Award, the Pulitzer Prize for drama, a Grammy and the Edward M Kennedy Prize for Drama Inspired by American History.
It also earned Miranda a MacArthur Foundation "genius" grant.
The show played the Kennedy Center in 2018 during Trump's first administration and again in 2022 when Joe Biden was president. It was scheduled again March 3-April 26, 2026. Those plans are now off. Tickets had yet to go on sale.
"We are not acting against his administration, but against the partisan policies of the Kennedy Center as a result of his recent takeover," said Seller.
"These actions bring a new spirit of partisanship to the national treasure that is the Kennedy Center."
The Kennedy Center has been in upheaval since Trump forced out the centre's leadership and took over as chair of the board of trustees. His decision to do so is part of his broad campaign against "woke" culture.
Actor Issa Rae, singer-musician Rhiannon Giddens, author Louise Penny and the rock band Low Cut Connie also have cancelled scheduled Kennedy Center events.
Singer-songwriter Victoria Clark went ahead with her February 15 show, but on stage wore a T-shirt reading "ANTI TRUMP AF".
This is not the first time the musical has taken a political stance.
In 2016, the Hamilton cast delivered a curtain call appeal to Vice President-elect Mike Pence, who was in the Broadway audience, asking that the Trump administration "uphold our American values" and "work on behalf of all of us".
The Kennedy Center, supported by government money and private donations, attracts millions of visitors each year to a complex that features a concert hall, opera house and theatre, along with a lecture hall, meeting spaces and a "Millennium Stage" that has been the site for free shows.
