A masked man killed a teacher and a boy and wounded two others in a Swedish school on Thursday, stabbing them as he walked from classroom to classroom before being fatally wounded by police marksmen, officers said.

Local media showed what it said was a picture of the assailant carrying a sword and dressed in a black trench coat and helmet, posing for pictures with students shortly before the attack.

"We thought it was a joke, a Halloween prank or something, but it wasn't," one witness student told TV4.

Local media said the suspect's social media accounts showed extreme right tendencies.

Police would not give any details of his motive but said possible far-right sympathies were being looked into, as part of a broader investigation that was being assisted by Sweden's security service.

The Kronan school is in Trollhattan, an industrial town of about 50,000 inhabitants in western Sweden that has a large proportion of immigrants and has been plagued by high unemployment after the demise of car company Saab which was headquartered there.

Attacks in schools are rare in Sweden, with the last similar attack taking place near Gothenburg in 1961.

"This is a black day for Sweden," Prime Minister Stefan Lofven said in a statement.

Police arrived minutes after the attack, following trails of blood smeared across the school corridors to find the assailant.

Police said they had responded to an emergency call saying a masked man with a sword was on the premises and that a person had been attacked at a cafeteria.

They shot the suspect, in his early 20s, who died later of his injuries at a hospital. He had no criminal record.

Photos by a local news agency showed several ambulances and police cars on the scene as the emergency services dealt with distraught adults and teenagers. A police cordon was marked out with white tape.

The lower grades of the school were criticised this year by Sweden's education watchdog for failing to address problems in providing a safe and calm environment for students and staff, saying teachers struggled to conduct teaching in some classes.