An Associated Press reporter saw at least one person on the ground receiving medical treatment immediately afterward the incident, which occurred approximately two hours after violent clashes between white nationalists and counter-protesters.
The nationalists were holding the rally to protest plans by the city of Charlottesville to remove a statue of Confederate Gen. Robert E. Lee.
There were several hundred protesters marching in a long line when the car drove into a group of them.
President Donald Trump is tweeting about the violence that has erupted amid a white supremacist march in Virginia.
Trump tweeted Saturday that "we ALL must be united & condemn all that hate stands for." He then wrote "There is no place for this kind of violence in America. Lets come together as one!"
The demonstrations began Friday in Charlottesville with white nationalists marching through town and while carrying lit torches. The demonstrators then clashed with counter-protesters.
Some of the white nationalists cited Trump's victory as validation for their beliefs.
The White House was silent for hours about the clashes except for a solitary tweet from First Lady Melania Trump. The president has received previous criticism for being slow to condemn acts of hate done in his name.