When Madonna stepped out onto the mammoth stage constructed on Rio de Janeiro’s Copacabana Beach on Saturday night in a gleaming halo headpiece and black kimono, she was greeted by the largest live crowd of her four-decade career.

The free show, announced in late March, was a grand finale to the pop superstar’s latest world tour, which has delivered 80 performances since last October. Without ticket data, concert crowd sizes can be difficult to gauge; Riotur, the municipality’s tourism department, estimated that 1.6 million people flooded onto the 2.4-mile stretch of sand on Saturday that had been turned into a roughly $12 million playground surrounding the 8,700-square-foot stage.

It was the culmination of days of Madonna-mania in the city, where talk of the singer, 65, was inescapable. Her songs spilled out of stores and car stereos. Fans assembled outside her hotel and shouted her name. Updates about the concert, which was broadcast on the network Globo TV, dominated local media reports.

The spectacle in Rio was a milestone in Madonna’s career: the victory lap for her first stage retrospective, called the Celebration Tour, in which she chronicled her rise to stardom, performing hits like “Into the Groove,” “Like a Prayer” and “Ray of Light” with a cadre of dancers, four of her six children, and a wardrobe of elaborate costuming that recalled some of her most memorable looks.

“Here we are, the most beautiful place in the world,” Madonna announced early in the concert, indicating the ocean and the mountains around her. “This is magic.” Later, she expounded on her gratitude for her Brazilian fans. “You have always been there for me,” she said. “That flag: that green-and-yellow flag, I see it everywhere. I feel it in my heart.”

The two-plus-hour Rio show hewed closely to the Celebration show, with a few exceptions: Madonna added her 2000 track “Music” to the set list, rearranged as a samba with live drummers and a special guest, the Brazilian drag star Pabllo Vittar. “Live to Tell,” staged as a tribute to victims of AIDS, included photographs of the Brazilian musicians Cazuza and Renato Russo, and the actress Sandra Bréa. For “Vogue,” Madonna appeared in a sparkly dress in the colors of the Brazilian flag and was joined by the pop sensation Anitta, who helped “judge” the competitors strutting down the runway.

The show had lifelong Madonna fans — many of whom came dressed in homage to their heroine in cone bras and lace gloves — screaming and dancing along. Ernesto Magalhães, 42, adorned in the style of Madonna’s “Material Girl” era in a gown and boa while balancing on stilts, epitomized the exuberant spirit of the occasion: “I’ve been a Madonna fan since I was 8; I couldn’t miss this.” Surya Rossi, a 31-year-old illustrator, decided on a last-minute trip from Rio Claro, São Paulo, after coordinating with her cousin, and stayed with friends. “Madonna has been a tremendous influence on me, both as a feminist and an artist,” she said. “Her empowering history and approach inspire me.”

It was also something of a landmark moment for live concerts globally. At a time of astronomical ticket prices and rising production costs for major shows, a free concert attracting a crowd of this scale is exceedingly rare, especially in the United States. California’s Coachella festival, where a three-day general admission pass starts at about $500, draws up to 125,000 attendees a day. Musikfest, a mostly free music festival in Pennsylvania, welcomed about 1.3 million visitors over 11 days last year.

“To have a free show like that in recent years is relatively unheard-of,” Katelyn Yount, the director of festivals at AEG Presents, said of Madonna’s closing show. Hangout, an upcoming music festival on Alabama’s Gulf Coast that is among the annual events AEG produces, is capped each day at about 40,000 attendees, who pay more than $300 for a three-day pass.

If a performance of this magnitude was going to be held anywhere in 2024, it would probably be in Rio, where officials have experience with enormous crowds. In 2006, about 1.5 million people attended a free Rolling Stones concert at Copacabana Beach, Brazilian police and other authorities said at the time. An even larger crowd was said to have gathered for a Rod Stewart show there on New Year’s Eve in 1994.

The idea for the sprawling event was first planted two years ago, when Luiz Guilherme Niemeyer, an executive with Bonus Track, a live entertainment company based in Rio de Janeiro, approached Madonna’s managers after hearing about plans for the tour. The Rolling Stones concert in 2006 helped convince him that something like this was possible, he said.

Negotiations stalled until last year, when a Madonna show in Mexico City was announced — ticketed dates for the Celebration Tour ended up wrapping with five nights there at the Palacio de los Deportes — and Niemeyer resumed his efforts to convince the pop star’s representatives and secure funding.

“It was an ambitious project for everyone, aiming to attract the largest audience of her career, and I thought this would help me persuade her,” Niemeyer said in an interview last week.

The concert’s corporate backers include the Brazilian bank Itaú and Heineken, and the government has made a significant investment as well.

Preparation for Madonna-palooza had consumed a segment of the city in recent days. A week ago, cargo planes carried about 270 tons of concert material to the city, including costumes and gym equipment. Eighteen sound and video towers were built across the beach, and last Wednesday, 4,000 workers prepared the stage in scorching heat.

Because this was the only Celebration concert in South America — Madonna last toured there in 2012 — fans congregated from all over the continent. In the days leading up to the event, a Madonna impersonator, Izelene Cristina, danced to “La Isla Bonita” at a bus station as she welcomed travelers. She would not be attending the concert because excitement over the superstar’s performance had led to a flood of bookings.

“Such is the life of an artist,” she said. “You work to move and entertain people.”

On Monday, Madonna and her touring team of about 200 arrived in Rio, heading directly to the French Riviera-inspired Copacabana Palace, the luxury hotel near where the stage was built. Later in the week, crowds gathered as close to the stage as possible, as the pop star crossed a specially built footbridge from the hotel to the stage to rehearse with some of her dancers.

Social media was flooded with clips of Madonna running through songs including the opener, “Nothing Really Matters.” “Are you happy? Are you ready?” she asked the assembled crowd at one point. The response: wild cheering. “OK, just checking,” she replied.

At a press briefing ahead of the concert, officials discussed the safety concerns that can accompany an audience of that size and unpredictable weather on the shore. Last year, the Brazilian D.J. Alok scheduled what had been billed as the “concert of the century” on Copacabana Beach, but a storm led part of the crowd to scatter, and concertgoers were faced with rampant pickpocketing, a problem at least some faced on Saturday night as well.

Marco Andrade, a spokesman for the Rio police, told reporters that the department planned to deploy 3,200 officers at the Madonna concert, compared with about 900 for Alok’s event. He said that facial recognition technology would be used at inspection areas, in addition to drones to monitor the crowd. In the end, the audience stretched into the ocean as well — a collection of boats anchored in the waters near the venue.

The atmosphere on the ground Saturday night was like a World Cup event, street carnival and New Year’s Eve celebration combined. Street vendors offered shirts, hats, cups and fans adorned with Madonna’s face and rainbow colors, and a plethora of barbecue, grilled cheese, empanadas and the Brazilian cocktail caipirinhas were available. To fight the heat, a firefighter atop a fire truck sprayed a jet of water on the crowd.

As the show ended with a remix of her 2009 track “Celebration,” Madonna addressed the audience for a final time: “Thank you, Rio,” adding “obrigada,” the equivalent in Portuguese. She smiled and let go of a Brazilian flag, flipped a white veil over her head and descended beneath the stage.