Authorities did not release her name, but CBS Sacramento identified the student as Jo-Anne Butler, a 17-year-old. She defended her actions in an interview with the station.
"That's a racist and hateful symbol," Butler, who has been suspended from her school for a week and faces potential battery charges, told CBS Sacramento about the hat. "Maybe just wake people up in some type of way, because it's not cool the environment our classroom is in."
Her father, Chris Butler, told the station that he did not approve of the disruption or the alleged actions of his daughter.
"But," he said, "as far as the issue being brought up, maybe this is something that needs to be brought up."
The El Dorado County district attorney's office said they only take action in cases with minors if they are referred by the county probation department. That agency can resolve allegations through means beyond prosecution, like anger management or substance abuse programmes, assistant district attorney Joe Alexander said.
His office has not received information about the incident from the department, he said.
The El Dorado Union High School District said in a statement that student and safety is their "highest priority" and that it is cooperating with authorities.
The red MAGA hats, and variations that come in all colours, have become political symbols and stand-ins for the praise and criticism of Trump. That has led to tensions and high-profile incidents across the country, and often on campus.
Some MAGA hat-clad white supremacists marched in Charlottesville, Virginia, during a Unite the Right rally last August; counterprotester Heather Heyer was killed in violence surrounding that rally.
About a week later, high school students wearing similar hats created a disruption on the campus of Washington's Howard University, a historically black school.
And in September, a Georgia teacher sent home two students wearing "Make America Great Again" T-shirts, mistakenly believing that political slogans were banned from the school.
The school district later apologised and said the teacher "inappropriately" gave her political opinion in class.