An 18-year-old man armed with a sword carried out the attack at the Brinell School in Fagersta, northwest of Stockholm, while classes were in session on Friday.
One person was killed and three others were wounded, two of them severely.
Police said the suspect had been arrested and that the case was being investigated as murder and attempted murder.
The police said they had no reason to believe there were more perpetrators.
Vastmanland County, where the town is located, said the two seriously injured boys were ages 12 and 17.
A third person, also under 18, was slightly injured and had been discharged from a hospital, Swedish news agency TT reported.
On Saturday morning, about 70 people gathered at the memorial site that the municipality prepared, carrying flowers and lighting candles, TT reported.
Prime Minister Ulf Kristersson and leader of the opposition Social Democratic Party Magdalena Andersson were among those who paid their respects.
There was no official information on the attacker's possible motive.
Sweden's national police said that investigators have already carried out two house searches in connection with the suspect.
Many witnesses were expected to be interviewed as part of the investigation.
The region went into a state of emergency on Friday, but it had ended by Saturday.
Swedish Prime Minister Ulf Kristersson, in an earlier X post, lamented the violence in Fagersta "right after the summer break".
"We do not yet know what lies behind the act, but we know that the police are working very intensively," he said.
"Our thoughts are with all those affected."
Sweden has seen a series of violent school attacks over the years.
In 2025, 11 people, including the gunman, died after an attack at an education center in Orebro in central Sweden, leading the government to propose tougher gun laws.
It's considered to be the worst mass shooting in the country's history.
In 2022, an 18-year-old man attacked two female teachers with a knife and an ax in a school in Malmo, killing them.
In 2015, a 21-year-old local man rampaged through a school in the southern industrial city of Trollhattan, stabbing three people to death before being fatally shot by police.
Authorities called it a racist hate crime, saying he methodically selected dark-skinned victims at Trollhattan's Kronan school, where most students are foreign-born.
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