The woman, who has not been named, was fatally wounded at Corpus Christi Catholic College in Leeds, northern England.
She was taken to hospital but was subsequently pronounced dead, West Yorkshire Police said.
The force said a 15-year-old boy had been arrested in connection with the incident and was in custody.
Detective Superintendent Simon Beldon said there was no ongoing risk to pupils or staff.
"The situation is under control and officers... Are currently at the school and are liaising closely with staff.