The Ziegfeld Theatre — one of New York’s most storied movie theaters and host to Hollywood red-carpet premieres — may be facing its final curtain.

Moviegoers turning up at the Ziegfeld over the Memorial Day weekend — the start of Hollywood’s summer season — were shocked to find the doors locked. It reopened on June 1, but the theater soon went dark again until last Tuesday’s arrival of “The Amazing Spider-Man.’’

The Ziegfeld, New York’s largest surviving single-screen venue in a city that once boasted dozens, has frequently closed during slow periods in recent years or for special events. But prolonged shutdowns during the lucrative summer season have fans concerned about its survival.

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Corporate parent Cablevision announced in early May that it was putting its Clearview Cinemas chain, including the Ziegfeld, up for sale. Industry sources familiar with the situation estimate the Ziegfeld is losing around $1 million a year. For a long time, they say, the hefty operating expenses for the 1,131-seat theater were covered by the glitzy Hollywood premieres that have made the Ziegfeld one of the nation’s best-known theaters.

But there are far fewer such events since the 2008 recession, and sources say the increasing number of IMAX screens (now four in Manhattan) have siphoned off potential audiences for the blockbusters that were long the Ziegfeld’s bread and butter, going back to the original “Star Wars’’ trilogy.

Even with what many filmmakers regard as the best screen image (it’s equipped for digital as well as 35mm and 70mm) and sound in the city, the immaculately maintained Ziegfeld often draws sparse crowds.

A Clearview rep declined to discuss the Ziegfeld’s financial situation, saying the chain didn’t break out figures for individual theaters. But she said recent special events at the venue included not only premieres of films like “Madagascar’’ and “Men in Black 3’’ but a series of concert films and showing sporting events like Rangers playoff games live on the big screen

“In addition to showing the latest blockbuster films, Clearview’s Ziegfeld Theatre is a landmark location for movie premieres and special events,’’ Clearview said in a brief statement. “It is normal course of business for the theater to be closed at certain times to accommodate these unique marquee activities.”

After The Post’s article provoked an outpouring of distress from the theater’s fans on Twitter, Clearview issued a second, one-sentence statement late Sunday afternoon: “We have no plans to close the Ziegfeld Theatre.”

Back in the 1970s, the Ziegfeld hosted road-show engagements with pricier tickets that ran for months. These days, on the rare occasions studios make such exclusives available — like the Ziegfeld’s lucrative 2006 run of “Dreamgirls,’’ with a then-unheard-of ticket price of $20 — it’s usually for two or three weeks at most.

For a time a few years ago, the Ziegfeld was a popular venue for Disney animation. Back in 2009, tickets for the Ziegfeld’s exclusive run of “The Princess and the Frog’’ went for as much as $50, including a “Disney Experience’’ held at Roseland.

Movie-theater historian Ross Melnick of CinemaTreasures.com said a takeover by Disney — which operates El Capitan, an old movie palace in LA — might be a “best possible outcome’’ for the Ziegfeld. But a spokesman for Disney, which bypassed the Ziegfeld for the current run of Pixar’s “Brave,’’ said the company has “no present interest’’ in the theater.

Unlike El Capitan, the Ziegfeld doesn’t have a full stage or orchestra pit — it’s a far less ornate homage to ’20s movie palaces with red velvet curtains that opened in 1969. The old Loews Astor Plaza, a similarly sized theater from the same era that closed in 2004, was renovated into a concert venue currently known as the Best Buy Theater.

A potential obstacle to any adaptive use is that Clearview reportedly has only about 12 years left on its lease for the Ziegfeld, which shares ownership with the nearby Alliance Bernstein skyscraper on Sixth Avenue, built on the site of a demolished theater erected by its namesake, producer Florenz Ziegfeld, in 1927.

“The real estate is so valuable, the city would probably just as soon have another hotel on the site than a really special place to see movies like the Ziegfeld,’’ said freelance film programmer Shade Rupe. “When Madonna had a premiere for her recent movie at a multiplex, it’s just wasn’t the same thing.’’