“This is thrilling,” Hillary Clinton, the former secretary of state, said on a chilly Thursday night outside the Music Box Theater on 45th Street, as women in strapless gowns walked a purple carpet.

Ms. Clinton, a noted Broadway superfan, was making her Broadway producing debut with “Suffs,” a new musical about women’s suffrage that traces the campaign for the right to vote from 1913 through the ratification of the 19th Amendment in 1920, which was celebrating its opening night.

The show not only arrives in a presidential election year, as states attempt to tighten voting laws, but also as Broadway is bringing more female-centric stories to the stage. Audience interest in such stories has also been strong — in the previous week, “Suffs” ranked in the top 10 of the 36 shows on Broadway in the percentage of its seats filled.

“I’m so excited that audiences are embracing this story,” Ms. Clinton said. “It’s historic and relevant, and it’s emotional, and it shows the relationships among these women who fought so hard to get us the right to vote.”

“And,” she added, “I literally hum the songs all the time.”

“Suffs” also boasts mainly women behind the scenes. Its core producing team, which is all female, includes Malala Yousafzai, the 26-year-old Pakistani activist and Nobel Peace Prize winner, who, like Ms. Clinton, is making her producing debut.

“This show reminds us that women fought hard for their right to vote, and it’s not something that we should take for granted,” said Ms. Yousafzai, who attended Thursday night’s performance with her husband, Asser Malik, and wore a red pin with a hand and a black heart — used to signify support for a cease-fire in Gaza — and a purple hijab.

Ms. Yousafzai said it was the musical “Matilda” that helped her adjust to life in the United Kingdom after she moved there after the Taliban shot her in Pakistan in 2012 because of her support of educational rights for girls.

“I could see another girl from another place, and I could relate to her,” Ms. Yousafzai said. “And I’ve been watching musicals ever since.”

When she saw “Suffs” at the Public Theater in 2022, and “immediately fell in love with it,” she knew, she said, that she had to be involved with bringing it to the Broadway stage.

“This was a story that everybody needs to see and everybody needs to hear,” Ms. Yousafzai said.

Shaina Taub, a singer-songwriter who wrote the book, music and lyrics, began working on the project 10 years ago, and plays Alice Paul, one of the leaders of the movement, in the show. It went through several years of development before premiering Off Broadway at the Public Theater in 2022, then still more rewrites, including a new opening number, before beginning performances on Broadway in March.

“I’m just excited for us to finally get to build up community around the show,” Ms. Taub said.

(The crowd on opening night included the filmmaker Ken Burns; the editor Anna Wintour; the influencer Dylan Mulvaney; and the performers Sara Bareilles, Ben Platt, Laura Benanti and Lin-Manuel Miranda.)

For two and a half hours, they listened to a cast that included the Tony Award nominees Jenn Colella and Emily Skinner race through a lineup of rousing feminist songs as Ms. Taub’s character, Alice, enlists her fellow suffragists. (In his review, The New York Times’s chief theater critic Jesse Green described the production as “smart and noble and a bit like a rally.”)

At the curtain call, Ms. Clinton, who was seated on the front right side of the center orchestra section, was one of the first to stand and applaud. As the cast and creative team were presented with white roses, Ms. Taub spoke from center stage.

“If you’re inspired by this story, if you do one thing, make sure you’re registered to vote,” she said, to raucous applause.

As the show let out, members of the cast, creative team and audience headed to Pier Sixty, an event venue on the Hudson River in Chelsea with floor-to-ceiling windows and a glass-enclosed terrace with a twinkling view of Lower Manhattan.

Ms. Clinton was one of the first partygoers to arrive. She relaxed and sipped from a glass of white wine until the cast walked in. She hugged Ms. Taub and congratulated her, while Ms. Yousafzai and her husband posed for photos in front of a purple “Suffs” backdrop.

The performers Ben Platt, Darren Criss and Rachel Brosnahan chatted around buffet tables stacked with an assortment of small bites, including barbecue glazed short ribs, miniature citrus crab cakes, raspberry cream tarts, tiramisù, lemon coconut macarons and carrot coconut bundt. Bartenders poured glasses of sparkling wine and Old Fashioneds.

Guests, who were given light blue sweatshirts that read “Ambitious” as they departed, seemed to absorb the message of the night.

As the party was picking up, a young woman in a gold-sequined dress posed near one of the large purple “Suffs” photo backdrops. Then she turned to a friend and said, “I’m going to vote!”