Another woman and a child were reportedly injured in the attack. The two injured were taken to hospital after the attack. The woman was reportedly stabbed in the chest.
The dead woman was a teacher at the school, and the injured are said to be another teacher and a student, Slovak media report.
The suspected perpetrator is said to be an eighth-grade student at a primary school in the northwestern part of the country.
The situation is now under control, according to police.
President Peter Pellegrini says he is "shocked by yet another case where a student attacks a teacher and a classmate."
In recent years, two more cases of fatal knife violence at schools have shaken Slovakia.
