Mayor Michael Signer confirmed the fatality on Twitter, urging "all people of good will" to return home.
It is unclear if the driver targeted the group or was involved in a traffic-related accident.
Video of the incident shows a car speeding down a narrow street filled with protesters before slamming into protesters and sending them ariborne, ultimately stopping only when it hit a line of cars. The driver then put the car in reverse and zoomed away.
It is unclear if the driver has been taken into custody.
Speaking from his New Jersey golf club, President Donald Trump condemned "this egregious display of hatred, bigotry and violence on many sides".
White nationalists were protesting the looming removal of a Robert E. Lee monument from Emancipation Park.
Lee was the rebel confederacy's top general in America's civil war, and calls have grown for confederate symbols to be removed from public spaces after a series of violent attacks that have been tied to white nationalists/supremacists, which regularly use such imagery.
On Friday night they marched through the University of Virginia campus holding torches in a scene reminiscent of Ku Klux Klan gatherings that haunted America's civil rights movement.
“You will not replace us”, and “Jew will not replace us” were chanted as an eerie torchlight glow enveloped the campus.
Former Klan Imperial Wizard David Duke attended the rally as well as other prominent white nationalist leaders.
University President Teresa A. Sullivan strongly condemned the rally, saying in a statement she was "deeply saddened and disturbed by the hateful behavior displayed by torch-bearing protestors that marched on our Grounds".
The two-day protest is thought to be the largest recent gathering of white nationalists.
Activists have warned of an emboldening of the group since Trump won last year's presidential race. And hate incidents targeting minorities have soared this year.
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