The man, identified as Jacob Blake, was hospitalised in a serious condition on Sunday evening after police shot him multiple times, according to local media.
Reports on social media on Sunday showed crowds had gathered at the scene of the shooting and thrown bricks and Molotov cocktails at police.
“Tonight, Jacob Blake was shot in the back multiple times, in broad daylight, Kenosha, Wisconsin,” Tony Evers, the state’s governor, said in a statement.
“While we do not have all of the details yet, what we know for certain is that he is not the first Black man or person to have been shot or injured or mercilessly killed at the hands of individuals in law enforcement in our state or our country.”
Mr Evers added: “We stand with all those who have and continue to demand justice, equity, and accountability for Black lives in our country ...
“And we stand against excessive use of force and immediate escalation when engaging with Black Wisconsinites.”
Police said the shooting happened at about 5pm local time in Kenosha as officers responded to a “domestic incident”.
The victim was immediately taken to a hospital by the police, according to a statement issued by the Kenosha police department.
Officers gave no further explanation for what led to the shooting - which will be investigated by the Wisconsin Department of Justice.
A video circulating on social media and cited by US publications showed a man walking towards a car followed by two officers, before one of the officers shot him as he opened the car door.
Seven shots could be heard on the video, although it was unclear how many times the man was hit and if more than one officer fired.
Kenosha County declared a state of “emergency curfew” on Sunday night, which the Kenosha Sheriff's Department would enforce until 7am, following protests over the shooting.
Protesters in the city were seen marching along lines of cars honking on their way to the local police station on Sunday, while one man was seen breaking the window of a patrol car parked along the street.
Outside the station, demonstrators clashed with officers who were dressed in riot gear and used plastic shields and batons to occasionally push people back.
The scenes in Kenosha were the latest examples of protests against police brutality and racism in the US following the death of George Floyd and other black people who have been killed by police.
Additional reporting by agencies
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