Aftonbladet says the shootings took place next to a police station so officers were on the scene immediately.
Police said a dozen shots were fired but no arrests have been made and they are looking for a dark vehicle.
Malmö police said shortly before midnight that an 18-year-old had died in hospital, and around half an hour later they confirmed that another one of the injured, a 29-year-old, had also died.
Swedish police said there was no cause for the public to be alarmed after a several people were shot in Malmo in southern Sweden, news agency TT reported.
Pictures from the scene of the shooting show armed officers as well as a large paramedic presence.
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A shooting has happened in Malmo, Sweden. Reports said they were searching for a dark-coloured vehicle.
Local police have released a statement which reads: 'Police were called to Drottninggatan [Queen Street] due to an outdoor shooting.
A police spokesman told AFP that the possibility of a terrorist link to the attack had been discounted.
The condition of the wounded remains unknown.