The parade on Wednesday to celebrate the Kansas City Chiefs’ Super Bowl victory brought hundreds of thousands of people to the city’s streets, a sea of fans clad in the team’s trademark red.

But when gunfire began near Union Station, a downtown transit center and tourist hub, around 2 p.m. local time, chaos erupted. Many attendees said it was hard to know where to go.

At first, the shots sounded like fireworks, said Ian Johnson, who had been selling hot dogs near the main event stage. Only when fans started running — some of them took shelter under his hot dog tent — did he realize that a shooting was underway.

Courtney Brown, of Independence, Mo., and her two sons were also near the stage when the gunfire began. She didn’t hear shots, she said. But she did hear someone shout: “Get down.”

Her instincts told her to flee, so she told her children to keep moving. “We were almost trampled twice,” she said. The three of them locked arms and huddled near a barricade until the crush of the crowd had eased.

Adrian Robinson had traveled to Kansas City from Gary, Ind., to sell T-shirts. He heard what he thought was a few firecrackers popping, and then he saw hundreds of people running down the street. A minute later, the same people were running back in the opposite direction.

“People were traumatized, man” Mr. Robinson said. “They were crying. Hyperventilating.”

The police said that they had detained three people after the shooting. But as the crowds began to disperse, some parade attendees were left stranded.

Zachary Dial and his family had traveled from Richmond, Mo., and parked in a garage by Union Station. A few hours after the parade was over, their car was still off limits, stuck behind crime scene tape, he said.

Quinton Lucas, the mayor of Kansas City, had also been downtown for the celebration. “I was there with my wife; I was there with my mother,” he said at a news conference on Wednesday afternoon.

“We never would have thought that we, along with Chiefs players, along with fans, hundreds of thousands of people, would be forced to run for our safety today.”

Traci Angel and Colbi Edmonds contributed reporting.