The photo was taken as Todd Whitmire, principal of
Whitmire said he was trying to restrain the girl, not choke her.
"I had separated her, and she began struggling, and I was pushing her away to get her away from the area, and she fell down," he told the newspaper.
The girl, Ashley Johnson, said Whitmire used too much force.
KTVU showed Johnson at home on Tuesday wearing a neck brace.
She told the TV station that the fight began when a larger male student attacked her, slamming her into a wall. But she added that she holds Whitmire responsible for her injury.
"I wasn't fighting back," she told KTVU. "I was lying on the ground."
The news outlets said Whitmire suspended 10 students on Monday after they added comments to the picture and shared it on social media.
Whitmire called the comments racist and derogatory and said they amounted to cyberbullying.
Johnson and the male student were also suspended for fighting.