It was almost 2 a.m. Monday when Orin Wolf, the producer of “The Band’s Visit,” stepped onto the dance floor at the Bryant Park Grill, a microphone in his left hand and a Tony Award in his right.

There was falafel and hummus on the buffet table, and the D.J. was playing a dance remix of “Sidi Mansour,” a Tunisian folk song. Ossama Farouk, a member of the show’s band, and his brother Sam were keeping time on the doumbek, a type of Egyptian drum, but they stopped when Mr. Wolf began to speak, trying to make sense of the musical’s Tonys sweep just hours earlier. (Standing 6 feet 5 inches tall, he’s easy to pick out in a crowd.)

“This show is about unity,” Mr. Wolf said, reflecting on the show’s depiction of Arabs and Israelis who unexpectedly find a common humanity over a single night, “and this award is about unity.” Then he asked the cast and crew to pose for a photo, and gave an instruction few producers ever have the opportunity to give: “Raise your Tonys in the air.”

The scale of victory by “The Band’s Visit,” a quiet musical in which not very much happens, has stunned Broadway. The musical won 10 awards — more than “A Chorus Line” or “The Lion King” or “The Book of Mormon” or “Dear Evan Hansen.”

It won three of the four musical acting prizes, including for Tony Shalhoub as leading actor, even though his character only has one song and he has already left the cast to continue filming a television series.

It even won the award for best book, which had widely been expected to go to Tina Fey for “Mean Girls.” That show, as well as the Disney blockbuster “Frozen” — both far splashier, both pulling in far bigger audiences — were shut out completely.

“The world is getting louder and faster and funnier, and Broadway musicals — even the very artistic shows — are getting louder and louder, but my show doesn’t subscribe to that,” Mr. Wolf, a bearish 38-year-old Cleveland native, said in an interview. “I never say this show is easy, and I never claim you can just come in and sit back and we’ll entertain you. You have to lean in. But a lot of people do that, and get a lot in return.”

The origin story begins in 2007, when Mr. Wolf took his wife, who was born in Israel, to the Other Israel Film Festival at J.C.C. Manhattan on the Upper West Side. There was a new Israeli film playing that they wanted to see — “The Band’s Visit,” a fictional story about an Egyptian police orchestra that gets stranded for a night in an Israeli desert town.

Mr. Wolf was, at that point, a producer largely in his dreams. He had been working for years assisting other producers and running a booking firm he founded that sent small shows to opera houses and old vaudeville theaters around the country.

But he had produced a small play called “Blood in the Sink” as well as several spoken word artists and a hip-hop musical called “History of the Word,” and had become one of the first two students in a new program at Columbia University, the T. Fellowship, to train aspiring producers.

When he saw the movie, with all the silence and longing surrounding the musicality of the orchestra, he knew he wanted to theatricalize it.

“It was this bizarre cloud-clearing moment,” he said. “I live in a very gray, cloudy world, but as the credits were rolling, I turned to my wife and said, ‘I want to adapt this on stage’.”

Then began a long and frustrating effort to secure the rights, starting by cold-calling Sony, which distributed the film.

“At first they weren’t even answering, and then, because I was persistent, they called back and said, ‘The filmmaker’s not interested. Sorry.’”

He spent a year trying to persuade the film’s writer and director, Eran Kolirin, to meet with him. It did not go well.

“I thought it was a bad idea,” Mr. Kolirin said. “I thought it would be embarrassing, seeing the characters start to sing, and it would be this big American thing which would not correspond with the spirit of the show.”

But Mr. Wolf did not give up, and Mr. Kolirin relented. “It was an exercise in letting go,” he said.

Then began the long slow process of developing the musical. For an initial reading at Hartford Stage in 2010, Mr. Wolf and the theater’s associate artistic director, Maxwell Williams, stitched together a script by slicing up translated drafts of the screenplay.

Separately, Mr. Wolf had started bundling investments for Broadway shows, most successfully for “Once” in 2012, earning credits as a co-producer.

In 2014, Itamar Moses, a playwright whose parents were from Israel, signed on as the “Band’s Visit” book writer, and David Yazbek, a songwriter whose father was from Lebanon, as its composer. That summer came a reading at the Atlantic Theater Company, an Off Broadway nonprofit that had previously nurtured “Spring Awakening,” another seemingly offbeat musical that clicked.

“The ones that are the most risky are the ones that are the most exciting,” said Neil Pepe, the Atlantic’s artistic director. “I found the story incredibly compelling and unexpected.”

The storied producer and director Hal Prince, who had become a mentor to Mr. Wolf through the Columbia program, agreed to direct the show, and a full production was announced by the Atlantic. But the schedule for Mr. Prince’s retrospective musical, “Prince of Broadway,” conflicted, and he dropped out. The show had to be delayed, and the creative team found a new director, David Cromer, whose Off Broadway production of “Our Town” had impressed Mr. Wolf.

Along the way, Mr. Wolf, who unlike many producers does not have personal wealth, took a job as president of NETworks Presentations, a Maryland-based company that produces tours of many Broadway shows, including “The Phantom of the Opera” and “The King and I.”

“I’ve always had to earn a living — I’ve always worked,” he said. Going to NETworks was a perfect marriage of things I’m passionate about.”

It also helped him meet theater leaders, to whom he has turned for guidance. “I’ve really grown up in this industry,” he said.

The Off Broadway production of “The Band’s Visit” opened to ecstatic reviews in the Atlantic’s 199-seat main theater in late 2016. “All of a sudden people were throwing money at me,” Mr. Wolf said. “Capitalizing it was a cinch.”

Among those new co-producers was Marc Platt, a television and film producer best known on Broadway as one of the lead producers of “Wicked” (and as Ben Platt’s dad), who became another key adviser to Mr. Wolf.

“I thought it was beautiful and perfect and quiet — it’s the quietest musical I’ve ever experienced — and I thought it was imperative that it come to Broadway,” he said. “It deserved to be put on the commercial map, and for people to experience it.”

Powered by an $8.75 million capitalization — much lower than the costs of its competitors — it transferred to the 1,039-seat Ethel Barrymore Theater on Broadway last fall; again, the reviews were rapturous. The musical has been selling well — it has surpassed its running costs every week thus far — but not nearly as well as the biggest shows.

Mr. Wolf is now preparing for a major casting change. Sasson Gabay, an Israeli film star who originated the role of the Egyptian orchestra leader in the movie, has agreed to succeed Mr. Shalhoub in the role, and is now in rehearsals.

He is also preparing to move to New York from Silver Spring, Maryland, where he’s been living during the show’s journey. He and his family have bought a home in Northern Manhattan, in part so they can be closer to the heart of the theater industry. “I want to be here because I want to keep doing this,” he said.

Follow Michael Paulson on Twitter: @MichaelPaulson.

A version of this article appears in print on , on Page C1 of the New York edition with the headline: ‘Raise Your Tonys in the Air’. Order Reprints | Today’s Paper | Subscribe