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.
In Europe the average is 1.6 people per million inhabitants.
This year shootings have also spread outside the country's main cities, as gang violence - which police say is often related to the shootings - spreads further afield.
Poor integration of immigrants, a widening gap between the rich and poor, and increasing drug use are what police say are the root causes of the violence.
Earlier this year the Swedish Prime Minister Magdalena Andersson also said a lack of integration had led to gang violence.
After a recent spate of shootings in the smaller city of Orebro, the local police chief said they now had more gangs - and they had become more violent.
"Where maybe 10 years ago they gave someone a beating, they then switched to shooting each other in the legs," Mattias Forssten told Reuters. "Now they shoot each other in the head."
The issue has become paramount to Swedish voters, with 41% of them saying crime is their biggest concern, according to Gothenburg University's Society, Opinion and Media Institute, cited by Reuters.
This could be problematic for the ruling Social Democrats, who critics say have failed to stop the rise in gang crime during their eight years in power.
The ruling party, however, say additional measures targeting criminal gangs as well as the expansion of the police force help will tackle the problem.