People at the Emporia shopping mall in the southern city of Malmo fled in panic after hearing around 20 shots being fired, Swedish outlet TV4 said.
Police have arrested a teenage boy and believe the shooting is related to gang tensions.
It comes as Sweden gears up for a general election next month, where gang violence tops voters' concerns.
Sweden still has one of the highest rates of gun killings in Europe.
An official Swedish government report published last year stated that four in every million inhabitants die in shootings each year in Sweden.