The two women, both in their 50s, “were employees of the school”, the police said in a statement following the attack at Malmo Latinskola, a secondary school in the centre of Malmo, the country’s third largest city.
Local media said the alleged attacker called the emergency number to say where he was and that he had put down his weapon and admitted to having killed two people.
He was armed with a knife and an axe, according to several Swedish media.
The suspect was arrested without difficulty shortly after the arrival of the first patrol, according to the police account.
Earlier in the evening, police had initially reported two injured among the around 50 people in the school at the time of the incident.
The two victims “were taken to the hospital but their lives could not be saved”, the authorities said.
Police were alerted around 5:15 pm (1615 GMT) and a first patrol was able to enter the school.
Footage shows heavily equipped and armed police inspecting the interior of the building.
The school remained cordoned off with police tape several hours later, and numerous police cars and ambulances were still at the scene.
After initial reports of screaming in the school, “we have had more information that pointed to a serious crime being committed and that violence was occurring in the school,” police spokesman Nils Norling told AFP.
“The first police patrol on site was able to arrive at the school and arrest a male suspect. They were also able to see that there were two injured people inside the school,” he said, speaking in front of the building.
No motive has been established so far.
After extensively inspecting the scene and interviewing witnesses, the authorities are convinced the suspect acted alone.
“A lot of work remains ahead of us to understand what happened and the motivation behind this appalling act,” said Asa Nilsson, one of the heads of the investigation.
A press conference is scheduled for 9:30 am (0830 GMT) Tuesday.
In January, a 16-year-old boy was arrested after wounding a student and a teacher in the town of Kristianstad, also in southern Sweden.
The case had been linked to a similar attack in August in the town of Eslov, around 50 kilometres (30 miles) away, when a student attacked a 45-year-old school worker.
No link has been established at this stage with the Malmo incident.
In October 2015, three people were killed in a racially motivated attack at a school in the western town of Trollhattan by an assailant later killed by police.
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