Officials said they have had no reports of injuries to protesters. The truck driver was pulled from he cab and has been arrested.
Many of America's major cities remain under curfew orders as National Guard forces watch and patrol.
"You cannot start meting out extrajudicial punishment," one former police officer and criminologist said of incidents of excessive force.
Governor calls Ellison, who represented Minneapolis in Congress for more than a decade, the "best person" to pursue justice for Floyd's family.
Massive protests are taking place nationwide over the death of George Floyd. In Minneapolis, Minn., a truck driver drove into a crowd of demonstrators, scattering thousands of people. No one was injured in the incident, and the driver of the truck has been taken to a nearby hospital.