Several emergency crews were dispatched to the school in Spisska Stara Ves, where two people were discovered dead and a third was taken to hospital with medium-severity injuries, emergency services spokeswoman Danka Capakova told Reuters.
The emergency services said the victims were 51 and 18, both female, and the injured was an 18 year-old woman, she said.
The three attacked were a female teacher and two classmates, Interior Minister Matus Sutaj Estok said on Facebook.
"The 18-year old (male) student suspected of committing a serious act in Spisska Stara Ves was detained a very short time after the incident," the police said earlier on Facebook.
Estok, the minister of education and the chief of police headed to the scene in Spisska Stara Ves, a town of about 2000 people on the Polish border, 376km northeast of the capital Bratislava.
Serious violence is rare in Slovakia, a central European country of 5.4 million.
The country was shocked last May when Prime Minister Robert Fico was shot in an assassination attempt.
"No problem in the world can be resolved with a knife or any other weapon," President Peter Pellegrini said in a statement on Thursday.
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