The row, which happened at Largo High School in Upper Marlboro, Maryland, was "very, very disturbing," police Chief Jank Stavinsky said at a news conference Friday.
Prior to the alleged attack, there was "physical contact" between the teacher and the student, he said.
"The teacher then gets involved in a physical assault on that student," Stavinski said. "The nature of that attack was extremely violent and such behavior is criminal in nature."
The teacher was arrested on Friday, Stavinski said.
"I am extremely disappointed with the terrible actions that have taken place in our classroom today," said Monica Goldson, executive director of public schools in Prince George's County.
"It's important to know that we set high expectations and standards for our staff and students," Goldson said – "and what you saw in that video is not the hard work that over 10,000 teachers do every day."
According to police, neither the student nor the teacher needed medical help. At least 30 students and 8 administrators are part of the investigation, Stavinski said.
The teacher was identified by police Saturday as 36-year-old Vivian Nori. She faces charges of child abuse and second-degree assault.
CNN could not immediately be reached for comment on Noire on Sunday and was unable to determine if it had legal representation.
The detectives have indicted the student in a juvenile court system, police said in a statement Saturday.
The student was upset that the teacher called her parents the night before and approached the teacher, police said, citing the results of a previous investigation.
"During that meeting, the student admitted to stepping on the teacher's leg and thrusting himself into the teacher's shoulder," the statement said. "The teacher then hit the student repeatedly."
After the two separated, police said, "the student grabbed the teacher from behind and punched her multiple times before splitting again."
CNN's Artemis Mostagian contributed to this report.