Police said a 13-year-old suspect was in police custody and that the situation was under control and there was no further threat to the public.
A motive was not immediately known.
The stabbings took place in Staškov, a small town near the border with the Czech Republic and Poland that has a population of about 2750 people.
The killed teacher was a 61-year-old woman.
The injured included a pupil who was in critical condition and a 41-year-old female teacher who was hospitalised with serious injuries, Slovakis' rescue service said.
President Peter Pellegrini said he was "deeply saddened by the tragic incident" at the school in Staskov.
He and Prime Minister Robert Fico offered condolences to the victims' families.
"Such events serve as a serious warning to our entire society," Pellegrini said.
"It is all the more important that we pay close attention to the atmosphere we create in society. We need more calm, respect, and mutual regard."
Interior Minister Matúš Šutaj Eštok, Education Minister Tomáš Drucker and Health Minister Kamil Šaško travelled to the town.
In 2025, an 18-year-old student fatally stabbed a 51-year-old deputy principal and an 18-year-old student at a high school in northern Slovakia.
In 2020, a 22-year-old former student attacked a high school in the town of Vrutky, killing the deputy principal and wounding five people, including two students.
In 2022, a high school student attacked and injured a female student at a high school in Novaky.
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