Thousands of people filled Manhattan’s Union Square Friday afternoon for an internet personality’s hyped giveaway that got out of hand, with some in the crowd clambering on vehicles, hurling chairs and throwing punches, leaving police struggling to rein in the chaos.

Aerial TV news footage showed a surging, tightly packed crowd running through the streets, scaling structures in the park and snarling traffic. Shouting teenagers swung objects at car windows, and some people climbed on top of a moving vehicle, falling off as it sped away. Others pounded on or climbed atop city buses.

By 5:30 p.m., police officers in growing numbers had regained control of much of the area, but small skirmishes were still breaking out, with young people knocking over barricades and tossing bottles and even a flower pot at officers. Police were seen wrestling people to the ground and chasing them down the street.

The NYPD didn’t immediately have information on injuries or arrests. Numerous people were in hand restraints, sitting on the sidewalks, and at least one young man was led away by two officers. Police formed lines in the street to try to direct the crowd.

On his Instagram feed, the streamer Kai Cenat had an image promoting a giveaway at 4 p.m. in the park. Some young people leaving the park said they had come expecting to get a computer for livestreaming and a new PlayStation.

Skylark Jones, 19, and a friend came to see Mr. Cenat and try to get something from his giveaway, which they said was promoted as a chance for things like gaming consoles or a gaming chair, as well as an opportunity to see the popular streamer.

When they arrived the scene was already packed, bottles were being thrown by people in the crowd and there was a commotion even before Mr. Cenat appeared, they said.

“It was a movie,”Mr.  Jones said. Police “came with riot shields, charging at people.”

Mr. Cenat, 21, is a video creator with 6.5 million followers on the platform Twitch, where he regularly livestreams. He also boasts 4 million subscribers on YouTube, where he posts daily life and comedy vlogs ranging from “Fake Hibachi Chef Prank!” to his most recent video, “I Rented Us Girlfriends In Japan!”

His 299 YouTube videos have amassed more than 276 million views among them. In December he was crowned streamer of the year at the 12th annual Streamy Awards. Messages sent to his publicist, management company and an email address for business inquiries were not immediately returned.

Livestreaming on Twitch from a vehicle as the event gathered steam, Cenat displayed gift cards he planned to give away. Noting the crowd and police presence, he urged, “Everybody who’s out there, make sure y’all safe. … We’re not gonna do nothin’ until it’s safe.” 

Eventually he and an entourage got out of the vehicle and hustled through an excited crowd, crossed a street and went into the park before the stream cut out.

The manager of nearby eyeglass shop Petite Optique, Carina Treile, was forced to remain in her store after it closed because police were still clearing the scene outside.

“Usually with people giving away free stuff, it’s never like this. It’s very organized,” she said. “And here we have a very chaotic scene.”

Ms. Treile said there were some loud bangs at some point, which frightened some in the crowd.

“That was a little bit scary, especially when people started running.”

Police, some with batons, used metal barricades to push the crowd back and loudspeakers to issue a warning: “This gathering is unlawful. You are ordered to disperse.”