"There was a large number of people carrying sticks and rushing to either get into the melee or see what was going on," Harvey said.
Police were investigating two assaults that happened outside the Capitol grounds, but no arrests have been made, the Sacramento Police Department said in a statement.
The Capitol was on lockdown until protesters cleared the area.
Videos from the melee posted on social media showed mounted officers dispersing a group of mostly young people, some with their faces covered, while some threw stones toward a man holding a stick and being shielded by police officers in riot gear.
A KCRA-TV reporter and his cameraman were caught in an altercation with protesters, who shouted "no cameras" as they tried to grab their equipment and shove them away from the crowd.
The victims were all present while the protest took place, said Sacramento police spokesman Matt McPhail, but he said it was still unclear whether and how they were involved.
The Traditionalist Worker Party had scheduled and received a permit to rally for two hours in front of the Capitol. Law enforcement was aware of the counterprotest effort and police deployed more than 100 officers to the Capitol, McPhail said.
The Southern Poverty Law Center has described TWP as a group formed in 2015 as the political wing of the Traditionalist Youth Network, which aims to "indoctrinate high school and college students into white nationalism."
Matthew Heimbach, chairman of the Traditionalist Worker Party, told the Los Angeles Times that his group and the Golden State Skinheads organized the Sunday rally. Heimbach said that in the clash, one of their marchers had been stabbed in an artery and six of the counterprotesters had also been stabbed.
Vice chairman Matt Parrott, who was not present at the Sacramento rally, blamed "leftist radicals" for instigating the violence.
A message left at a phone number for the Traditionalist Worker Party was not immediately returned to the Associated Press.
A post recently uploaded to the site of the Traditionalist Youth Network said TWP members planned to march in Sacramento to protest against globalization and in defense of their right to free expression. They said they expected to be outnumbered 10-to-1 by counterprotesters.
"We concluded that it was time to use this rally to make a statement about the precarious situation our race is in," the Traditionalist Youth Network statement said. "With our folk on the brink of becoming a disarmed, disengaged, and disenfranchised minority, the time to do something was yesterday!"
The clash follows a confrontation in March between Ku Klux Klan members and counterprotesters in Anaheim, in which three people were stabbed.