The Express quoted a Swedish policespokesman as saying: "We have received several reports of a shooting in Trelleborg".
Police spokesman Fredrik Bratt said: "We get calls from several people who have heard shots in central Trelleborg".
There is no official word from the authorities regarding the suspect, whether there is more than one shooter or if anyone has been detained.
"We saw someone running outside".
Shortly thereafter, armed police arrived and cordoned off the crime scene, where witnesses had reported hearing a loud "bang".
Trelleborg is a Swedish port town located 33 kilometres south of Malmo and 64kms southeast of Copenhagen, Denmark.
At least four people have been taken to hospital and several others have been injured in the attack.
Security officials have blocked some areas and are conducting "an investigation".
Marcus Åberg lives in the area where the shooting occurred and was walking home with a few friends when he heard gunshots. "All of the injured are men", according to police. "I jumped really when I heard the shots", he told local media.
"Right now, it's locked off", he tells local media.