Harold “Hal” Prince, the producer and director behind many of American theater’s greatest musicals, died Wednesday. He was 91.

Prince’s publicist said he passed away after a brief illness while in Reykjavik, Iceland.

The Broadway impresario — known for helping bring the world “Fiddler on the Roof,” “Cabaret,” “West Side Story,” “Company,” “Sweeney Todd” and “The Phantom of the Opera” — was mourned by ­titans of theater.

“Farewell, Hal,” said collaborator Andrew Lloyd Webber.

“Not just the prince of musicals, the crowned head who directed two of the greatest productions of my career, ‘Evita’ and ‘Phantom.’ This wonderful man taught me so much and his mastery of musical theater was without equal.”

Broadway theaters — and those on London’s West End — dimmed their lights in his memory Wednesday evening.

“To be both a genius and a gentleman is rare and extraordinary,” said Thomas Schumacher, chairman of The Broadway League.

“Hal Prince’s genius was matched by his generosity of spirit, particularly with those building a career.”

In a career that spanned seven decades and netted him 21 Tony Awards — more than any other individual — Prince had a hand in just about everything.

Starting as an assistant stage manager to legendary producer George Abbott, he had his first hit with 1954’s “The Pajama Game.”

What followed was a steady stream of successes — “Damn Yankees,” “West Side Story,” “Fiorello!,” “Fiddler” and “Cabaret.”

The latter’s leering, pansexual emcee first played by Joel Grey — and later Alan Cumming — was Prince’s creation.

As Prince told The Post in 2014, he was in postwar Germany with the US Army when he found his muse in a club with “a little tacky band and an emcee who was pathetic, vulgar and tragic,” surrounded by “three zaftig chorus girls in butterfly costumes doing their routines.”

Over the years, Prince’s collaborators included Leonard Bernstein, Stephen Sondheim, Jerome Robbins and Lloyd Webber, whose “Phantom of the Opera” is still running — thanks, some say, to Prince’s surprise visits to the Majestic Theatre, conveniently located right near his office.

A few years back, he wondered whether Carlotta the diva had skipped her high note. She had.

“Put it back in,” Prince decreed.

Hugh Panaro, a former Phantom, recalled one Christine who had an off night during one Prince visit. Her contract wasn’t renewed.

Prince is survived by his wife, Judy, children Daisy and Charles, and three grandchildren — as well as all the shows he helped bring to life that are still playing around the world today.

Prince’s family will honor his life with a party — rather than a funeral.

“As per his wishes, there will be no funeral but there will be a celebration of his life this fall with the people he loved most, the members of the theatrical community that he was a part of for seven decades,” a rep said.

Additional reporting by Max ­Jaeger, with Wires