Protests erupted in the US city of Kenosha, Wisconsin, after police shot a black man in the back several times from close range as he got into a car on Sunday evening, according to cellphone video of the incident.

The man, named as Jacob Blake by Wisconsin governor Tony Evers, was airlifted to Froedtert Hospital in Milwaukee and was in serious condition, Kenosha police said.

"Tonight, Jacob Blake was shot in the back multiple times, in broad daylight, in Kenosha, Wisconsin," Evers said on Twitter.

"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.

"We stand with all those who have and continue to demand justice, equity, and accountability for Black lives in our country."

Police said the shooting occurred when they were responding to a domestic incident at about 5:11pm.

Cellphone footage of the incident shows a black man followed by two police officers with guns drawn as he goes around the front of a gray SUV.

As he opens the door and tries to get into the driver's seat one of the officers pulls on his T-shirt and he appears to be shot repeatedly in the back.

Civil rights attorney Ben Crump said Blake's three sons were in the car at the time and he had been trying to break up a fight between two women.

"They saw a cop shoot their father. They will be traumatized forever," Crump said on Twitter.

Crump represents the family of George Floyd, a black man who died on May 25 when a white police officer knelt on his neck for nearly nine minutes.

After nightfall in Kenosha, a crowd of protestors faced off against riot police, according to footage posted by the Milwaukee Journal Sentinel.

Kenosha city later declared an overnight curfew.

Wisconsin Department of Justice said its criminal investigation division was investigating the shooting.

"The involved officers have been placed on administrative leave," it said in a statement early Monday.

The death of Floyd ignited massive nationwide protests against racism and police brutality.