The incident took place at a primary school in Zagreb, according to state news agency Hina.
Police said the attack happened just before 10am on Friday in the Precko neighbourhood.
They described the attacker as a “young male” and said he had been detained.
Emergency crews including paramedics and an air ambulance rushed to Precko Elementary School as authorities were alerted to the incident.
The teacher is said to have suffered life-threatening injuries and remains in hospital after undergoing surgery, according to State broadcaster HRT.
It reported the attacker entered the school and went straight into the first classroom he found and attacked the children.
Video footage published by Croatian media showed children running away from the school building.
Croatian media reports described the school as being “under siege” with students and staff left “in shock” and in tears.
At least one child died from their injuries, reported Dnevnik.hr, with a total of eight people injured including the attacker.
Health minister Irena Hristic confirmed one of the pupils who had been attacked had died.
The interior ministry issued a statement saying the attacker was aged 19. Local media reported he was a former student and was taken to a hospital by police officers and is said to be in a stable condition.
Prime Minister Andrej Plenkovic said at the start of today’s government session he was “appalled” by the attack and authorities were working to determine exactly what happened.
“We are horrified,” he said.
“We also express our regret and sympathy to the families of the injured children at the Precko Elementary School.”
The wounded had been taken to hospitals across the capital for treatment, he added.
“We are shocked by this terrible event and express our sympathy to all the victims and their families,” city officials said in a statement.
“This is a great tragedy for the City of Zagreb and for all of Croatia.
“The mayor and his deputies are at the scene. At this moment, the police are establishing all the circumstances, the perpetrator has been arrested.
“The city will help provide psychological assistance to students, parents and school employees.”
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