Police Chief Stacey Graves told a news conference three people were detained "and under investigation" in connection with the bloodshed near the city's landmark Union Station after a confetti-strewn parade.
Graves said investigators had no known motive for the gun violence. Eleven of those hurt by gunfire or the ensuing chaos were children as young as 6.
At least 22 people were struck by gunfire, one of them fatally, authorities said. Local radio station KKFI identified the slain victim as Lisa Lopez, one of its disc jockeys and host of the show "Taste of Tejano."
Fifteen victims suffered life-threatening wounds, Fire Department Chief Ross Grundyson said at a late-afternoon news conference.
Kansas City Mayor Quinton Lucas said the prevalence of firearms and gun violence in the United States made it difficult to provide complete security for any public event, even with several hundred law enforcement officers on patrol for the Chiefs' victory parade and rally.
"Parades, rallies, schools, movies - it seems like almost nothing is safe," Quinton, a Democrat, told reporters, recounting how he was among those who ran for cover at the sound of gunshots.
"We became part of a statistic of too many Americans, those who have experienced or been part of or connected to a mass shooting," he said.
Hours after the violence, the precise circumstances remained unclear, and authorities were still determining the full extent of casualties and age range of the victims.
Children's Mercy Kansas City treated a dozen people from the incident, 11 of them children aged 6 to 15. Nine of the 12 patients were gunshot victims, a hospital spokesperson said.
Graves said she was aware of reports that some fans may have participated in the pursuit and capture of at least one of the suspects, and investigators were reviewing video of the incident.
HEAVY POLICE PRESENCE
Some 800 law enforcement officers were at the rally and parade that preceded it, including agents of the FBI and the federal Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF).
All of the Chiefs players, coaches and staff who attended the victory rally were accounted for and safe, the National Football League team said in a statement.
The blast of gunshots, fired outside near a garage by the station, came at the end of the victory rally following a parade, according to police.
Video posted on social media showed pandemonium outside the station, with dozens of uniformed police officers, weapons drawn, running into the building as scores of bystanders fled in the opposite direction.
Rapid-fire gunfire was audible in footage posted online by ABC News.
Chiefs fan John O'Connor said in a video interview posted by the Kansas City Star that he ran with other members of the crowd into a garage after hearing 15 to 20 shots in quick succession, recounting, "It sounded like fireworks at first."
Union Station, a 109-year-old Beaux Arts building that once served as a major U.S. rail hub for passenger and freight traffic, is home to a museum and visiting attractions today, and is a terminal for Amtrak passenger service.
The Super Bowl celebration featured Chiefs tight end Travis Kelce on stage with quarterback Patrick Mahomes and other teammates, but Kelce's pop superstar girlfriend, Taylor Swift, was back on tour in Australia at the time.
Mahomes said on X: "Praying for Kansas City," followed by several praying-hands emojis.
Chiefs linebacker Drue Tranquill, who was at the parade, asked on social media for prayers: "Pray that doctors & first responders would have steady hands & that all would experience full healing."
A statement from the NFL said: "We are deeply saddened by the senseless shooting that occurred in Kansas City today following the Chiefs' celebration. Our thoughts are with the victims and everyone affected."
Missouri Governor Mike Parson and his wife were in attendance when the gunfire began, but were safe and secure following the incident, he said in a message posted to X, thanking law enforcement for its response.
Kansas Governor Laura Kelly was also present at the rally when the shots were fired.
As he has after so many previous mass shootings, U.S. President Joe Biden called for enactment of tougher gun control measures. Biden said he and his wife "pray for those killed and injured today in Kansas City, and for our country to find the resolve to end this senseless epidemic of gun violence."
The Chiefs on Sunday defeated the San Francisco 49ers in overtime to win the Super Bowl, 25-22, marking their fourth National Football League championship.
On June 17, 1933, Union Station was the site of an outdoor shootout and murder of four law enforcement officers and a criminal fugitive in a notorious incident known as the Kansas City Massacre.
Wednesday's violence took place on the sixth anniversary of one of the most notorious mass shootings in recent U.S. history, when 17 people were killed and 17 more were injured at Marjory Stoneman Douglas High School in Parkland, Florida. The shooter in that incident, a former student who was 19 at the time, pleaded guilty and was sentenced to life in prison.
Reporting by Steve Gorman in Los Angeles and Brad Brooks in Longmont, Colorado; Additional reporting by Daniel Trotta, Dan Whitcomb, Kanishka Singh and Rich McKay; Writing by Steve Gorman; Editing by Howard Goller, Lincoln Feast and Gerry Doyle