The violence broke out at shortly before 2am on Thursday night when a 20-year-old man was shot in the back at the Mobilia shopping centre near the town centre. He is now being treated in hospital for serious but not life-threatening injuries.
The next day shots were fired at apartments in the districts of Fosie, Ärtholmen and Rosengård, none of which left anyone injured.
"It's too early to say if they are connected, because we are working so hard this week, because we have had the explosions, and now we have had the shootings," said Ewa-Gun Westford, spokesman for the police in southern Sweden, told The Local.
The shootings came less than a week after a building in Gullvik, a leafy suburb of detached houses, was riddled with bullets last Sunday. Earlier last week, explosive devices went off outside two driving schools in the city.
"We don't think there is any connections to the shootings last weekend, we can't see anything, but it is rather early in the investigations," Westford said.
But judged by the Malmö police's press releases, the rate of shootings has since picked up, with seven this month, two in October and five in September.
The city in October launched a new 'Sluta Skjut', or 'Stop Shooting', programme, which builds on the Group Violence Intervention (GVI) strategy used with good results in many US cities.
Eleven young men have been killed in shootings in Malmö so far this year, and 26 since 2016.