Several hundred protesters were marching when the auto appeared to deliberately drive into a group of them, The Associated Press reported.
Fields is being held on suspicion of second-degree murder, malicious wounding and failure to stop in an accident that resulted in death.
Police in Virginia have arrested the driver suspected of plowing his vehicle into a group of counter-protesters in Charlottesville, killing one woman and injuring 19 people, five of whom are in critical condition.
In a brief appearance, US President Donald Trump condemned the violence and "hate" in the city.
- David Perdue (@sendavidperdue) August 12, 2017I strongly condemn the hatred and violence in Charlottesville.
Facts About North Korean Dictator Kim Jong Un
Following that vote, reports indicated that the country has developed a miniaturized nuclear warhead capable of fitting on a missile.
Fatal riots broke out in the liberal town of Charlottesville, home to the University of Virginia, after alt-right protesters descended on the area to protest the planned removal of a statue of Confederate general Robert E Lee.
Some criticised Mr Trump for his seeming reluctance to specifically blame the white supremacists.
Trump did not acknowledge the fatality in his public remarks on Saturday, a fact that drew criticism from prominent senators of both parties.
The FBI's Richmond field office, the Justice Department's Civil Rights Division and U.S. Attorney's Office for the Western District of Virginia said they have opened an investigation into the circumstances of the deadly vehicular incident.