The incident occurred on the first day of a return to in-person classess for students at Sutter Creek Elementary in the small town of Sutter Creek, east of Sacramento.
The school’s superintendent sent a letter to parents explaining what happened, which was obtained by NBC News.
According to Torie Gibson, the Amador County Unified School District Superintendent, the incident occurred just after school had let out for the day on Wednesday.
"As the first day of school comes and goes, there are always hiccups along the way, especially during this trying time," she wrote. "Unfortunately, a parent took it upon himself to verbally assault a principal that led to a serious physical altercation between him and a teacher as the teacher intended to protect the principal."
According to news outlet KCRA, the fight began because a parent was upset at the school's mask mandate.
The parent reportedly became incensed when he saw his daughter leave the school with a mask on her face, prompting him to confront the female principal. After the argument became heated, a male teacher stepped in to protect the principal.
At some point the encounter escalated into a brawl, which reportedly left the teacher bleeding.
Ms Gibson said the teacher received "lacerations on his face, some bruising on his face and a pretty good knot on the back of his head".
He was treated at the hospital and released the same day.
It is unclear what injuries the parent sustained but he has been barred from showing up at the school. The student will be allowed to continue attending.
The superintendent made it clear in her letter that "assaulting a staff member will never be tolerated on any school campus," and reaffirmed that mask "mandates are forever changing so understanding current requirements is critical."
She pointed out that she and the administration and teachers who work at the school do not make the rules regarding mask use.
"We are the ones required to follow/enforce them if we want to keep our doors open and students at school five days a week," she said.
Amador County Unified School District requires that all students wear masks while indoors unless they have a medical exemption.
The Sutter Creek Police Department released a statement on Facebook saying the incident was under investigation and asking for witnesses to the fight to come forward with information.
Ms Gibson said the school has filed a report with the police and will consider pressing charges against the parent once the police conduct their investigation.
The assault on the teacher is one manifestation of a broader debate raging around the country over whether or not students should be forced to wear masks while in school.
Childhood health experts fear that the highly contagious Delta variant of the coronavirus is going to spread unrestricted through school populations if mask mandates are not in place.
Anti-mask parents and protesters disagree, and see the masks as a political statement rather than a piece of cloth that can help keep their children safe.
A Kaiser Family Foundation poll recently found that the majority of parents in the US support having their children and unvaccinated staff wear masks while returning to school.
The results of that poll were consistent across racial borders and among Democrats and Independents. The only demographic that opposed mask wearing for students was Republicans.
The American Academy of Pediatrics has reported an increasing number of coronavirus cases in children.
However some state leaders have flexed their executive powers to prohibit school districts from requiring mask usage.
Florida's Republican Governor Ron DeSantis believes that Covid-19 does not pose a serious risk for students. He put that belief into action last month when he issued an executive order prohibiting mask requirements in schools.
While hospitalisations and deaths in children due to Covid-19 are rare, they are increasing due to the Delta variant.
The AAP is so concerned by the developments that it has asked the US Food and Drug Administration to fast-track an emergency authorisation allowing children under 12 to receive vaccines.
A group of 800 doctors wrote a letter to Governor DeSantis asking him to retract his order and to do more to encourage Florida's residents to take the shot.
The Republican Governor of Texas, Greg Abbott, issued a similar order. His colleague, Republican Governor Asa Hutchinson of Arkansas, also banned mask mandates, but has since said he regrets the move as coronavirus cases ravage the state.