The proposal had led to bitter backlash from the Jewish community and beyond because of the designer's past anti-Semitic and racist statements.
"John Galliano: Horizons," the high-profile spring Costume Institute exhibit that was to be launched by the annual Met Gala in May, will be replaced by another exhibit, the museum said on Monday.
"Following thoughtful discussions with John Galliano, we have together decided not to proceed with the exhibition," Max Hollein, director and CEO of the museum, announced in a statement.
"After much reflection and discussion with The Met and all those involved, I have decided, with great sadness, that it is best for the exhibition not to take place at this time," the designer said in the statement.
"I remain fully accountable for the pain caused by my words in the past, particularly the hurt I caused to the Jewish and Asian communities, and I remain deeply sorry for it."
Galliano, long recognised as one of the fashion world's biggest talents for his creatively flamboyant designs, was at the pinnacle of that world for years as creative director of Christian Dior.
He was fired from the post when a series of racist and anti-Semitic comments from 2010 and 2011 surfaced and went viral, leading to his conviction in an anti-Semitism trial in France.
Among the remarks Galliano made to bar patrons, circulated on video, were "I love Hitler".
He also told patrons, who were Jewish, that their mothers and forefathers would have been "gassed".
He also made derogatory comments to an Asian patron.
Dropped by Dior, Galliano spent several years involved in public and private efforts to rehabilitate his image.
He made a comeback in 2014 when he was hired by Paris fashion house Maison Margiela, where he remained for a decade.
He was to become only the third living designer to be honoured with a solo show at the Costume Institute.
The spring exhibit is launched each year by the star-studded Met Gala, the most visible event on the fashion calendar, where celebrity guests tour the show's galleries during cocktail hour.
The gala is overseen by Anna Wintour, Vogue's global editorial director and one of the most influential figures in fashion. Wintour has been a longtime supporter of Galliano.
In her own statement released by the museum, she called Galliano's decision to step aside a courageous one.
"John's decision that the exhibition devoted to his work should not take place at this time is very courageous and a measure of the man he is," Wintour said.
"I believe this is the right decision, and both he and the Museum have my full support."
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