In Stockholm, a 30-year-old man was shot dead in broad daylight in Tensta, a north-western suburb. Another man has life-threatening injuries.
Police are questioning several witnesses in an attempt to track the killer, who allegedly left the scene on a moped.
The attack took place at 6.30pm on Tensta Allé, a main road in an area that was part of the Million Homes Programme in the 1960s.
According to newspaper Aftonbladet, the shooter waited on a footbridge before firing at least seven shots. Police would not say whether they knew the victim.
In Malmö, two people were seen fleeing the scene after several shots were fired into an apartment in the central Värnhem district.
Bullet holes were found in the windows of the apartment, located just 15 metres from a police station.
Police are treating the attack as attempted murder, newspaper Sydsvenskan reports.
In Gothenburg, six cars were set alight overnight in different parts of the city. Police said the long distances between some of the buring cars meant it was likely there were different perpetrators, although they added there may have been some form of cooperation.
Witnesses to the incidents painted a similar picture: two to three youths wearing balaclavas or hoodies poured flammable liquid into the cars before setting them alight.
There have been no arrests in connection with the incidents in any of the three cities.