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.