The boy ran to a classroom, told a teacher and the two went to the office where school officials took pictures of the injuries.
Essick said red marks were still visible when deputies arrived a short while later.
"You can see fingerprints on his neck," Essick said.
Garcia-Bratcher was arrested Saturday on a charge of inflicting injury to a child. She was released later in the day on $30,000 bail.
She is scheduled to appear in court Thursday.
The woman told arresting officers she was on campus to enroll a third child in school, Essick said.
She spotted her 11-year-old son on the playground and asked him to identify the boy who was allegedly bullying her daughter, he said.
No adults witnessed the confrontation, and the woman had apparently not checked in with the office before coming on campus, authorities said.
Essick said deputies were looking into the bullying claims but so far have not substantiated them.
But, he said, even if bullying was occurring, Garcia-Bratcher had no business confronting the boy directly.
"To take it into her own hands was absolutely the wrong thing to do," Essick said.
Jennie Snyder, superintendent of Piner-Olivet Union School District, said it is rare to have a parent confront a student on campus.
"Thankfully, it's not something that occurs," she said.
She said policy requires visitors to sign in to the office and wear a badge.
A letter was being drafted about the incident and would be emailed to parents Monday, she said.
She also said she was looking into bullying claims.
"Student safety is our first and foremost concern," Snyder said. "We have safety procedures in place and we will be following through on them."
You can reach Staff Writer Paul Payne at 568-5312 or firstname.lastname@example.org