Footage posted online showed a red SUV driving through a Christmas parade in the city of Waukesha, west of Milwaukee,Wisconsin, at around 4.40pm (local time) on Sunday.
Chief of Waukesha Police Dan Thompson confirmed there were "some fatalities" and that dozens have been left injured during the incident.
It is understood one person is in custody.
In a press briefing, the chief of Waukesha Police told journalists: "We have a person of interest that we are looking into at this time."
Mr Thompson said the investigation is ongoing - with assistance from the Wisconsin Department of Justice - but a "suspect vehicle" has been recovered.
The Milwaukee Dancing Grannies, which had people taking part in the parade, posted on its Facebook page that "members of the group and volunteers were impacted and we are waiting for word on their conditions."
The group's profile describes them as a "group of grannies that meet once a week to practice routines for summer and winter parades."
Waukesha mayor Shawn Reilly told WITI television station in Milwaukee that he does not believe there is any current danger to the public.
A video taken along the parade route showed a group of what appeared to be teenage girls dancing with white pompoms and wearing Santa hats.
The vehicle then plows into the group as the person filming shouts, "Oh my God!" over and over. The video shows people tending to at least one of the girls on the ground.
Corey Montiho, a Waukesha school district board member, told the Milwaukee Journal Sentinel that his daughter's dance team was hit.
"They were pom-poms and shoes and spilled hot chocolate everywhere. I had to go from one crumpled body to the other to find my daughter," he said. "My wife and two daughters were almost hit. Please pray for everybody. Please pray."
In a statement on Facebook, officers added that a family reunification location has been established at the Metro Transit Centre by Bank Street.
Angelito Tenorio, a West Allis alderman who is running for Wisconsin state treasurer, told the Milwaukee Journal Sentinel that he was watching the parade with his family when they saw the vehicle come speeding into the area.
He told the newspaper: "We heard a loud bang, and just deafening cries and screams from people who are struck by the vehicle.
"Then we saw people running away or stopping crying, and there, there are people on the ground who looked like they'd been hit by the vehicle.
"It just happened so fast. It was pretty horrifying."
Mr Tenorio said he saw about 10 people, children and adults, on the ground who appeared to have been hit by the vehicle.
The parade is sponsored by the city's Chamber of Commerce. This year's edition was the 59th of the event that is held each year the Sunday before Thanksgiving.
Waukesha is a western suburb of Milwaukee, and about 55 miles north of Kenosha, where Kyle Rittenhouse was acquitted on Friday of charges stemming for the shooting of three men during unrest in that city in August 2020.