The girl was walking home alone from a friend’s house when the attack occurred.
According to the local Kvällsposten daily, the girl became aware that a man was following her and began to run towards Lindängeskolan but he caught up with her and trip her up.
The newspaper reports how the man is thought to have held a can with a strong smelling liquid, believed by the police to be chloroform or ether, under her nose so that she became dazed and eventually passed out.
He is then suspected of having raped the 12-year-old. The girl came to later that evening, but not before nightfall.
The newspaper reports that there were several patches of sperm on her clothing after the attack.
The police have secured a few leads but on Monday morning no one had been arrested. Police believe that the man has carried out several similar attacks.
Andres Kristenson, who is leading the investigation with the Malmö police, believes that there are strong chances of solving the crime.
“But I don’t want to give any further details,” he said to the TT news agency.
The case has been classified as aggravated rape. The man is reported to be around 30-years-old, 170 centimetres tall and was wearing black clothing.