Kenosha County Sheriff David Beth told the New York Times that one person had been killed.
The violence occurred during a confrontation between protesters and a group of armed men, the newspaper said.
Unrest broke out in Kenosha after Jacob Blake was shot by police on Sunday.
Footage shared online showed people running through the streets of Kenosha as gunshots could be heard. Other footage showed wounded men lying on the ground.
Further details of what happened were not immediately available.
The governor of Wisconsin is sending more National Guard troops to the city.
How have the protests unfolded?
Within hours of Mr Blake’s shooting, hundreds of people had marched on Kenosha’s police headquarters. Cars were later set alight, and police urged 24-hour businesses to consider closing because of “numerous” calls about armed robberies and shots being fired.
On Monday, Governor Evers called up the National Guard to aid local police and imposed a night-time curfew on Kenosha. Police backed up by the National Guard used tear gas, rubber bullets and smoke bombs, protesters said. Some demonstrators were seen attacking cars and property with baseball bats, news agency Reuters reported.
On Tuesday hundreds of protesters marched through the city. A small group threw fireworks and…