The explosive which was thrown at the block just after midnight on Saturday was powerful and damaged a large area of the building's façade and smashed a couple of windows.
The apartment that was the probably target for the attack was empty at the time, according to Hans Nilsson at Skåne police.
Mikael Persson at Skåne police confirmed that the attack has been linked to recent violence between two organized gang factions in the Malmö area.
No one had been arrested for the grenade attack by midday Saturday. A 23-year-old man, who is familiar to the police and resident in an apartment in the block, has been taken in for police questioning.
According to witnesses a loud blast and then something sounding like a gun shot was heard. Police found empty shells at the scene.
Recent weeks have seen a series of clashes between different gang factions in Skåne. On Wednesday night windows were smashed in a bomb attack against a restaurant in Lund. The restaurant was closed for the summer and no one was hurt when the bomb exploded by the entrance.
Police consider the Lund bomb attack to be part of an escalation of the ongoing gang war between two criminal groups in Malmö.
Only 24 hours prior a 22-year-old man was shot at on Tornfalksgatan in Malmö. Several shots were fired at his car but he escaped injury.
Since mid-summer at the end of June, when a 20-year-old man was serious injured in a shooting in Malmö suburb Persborg, a further seven or eight serious incidents have occurred in and around the southern Swedish city.
No one has yet been arrested for either of the two shootings or Thursday's bomb attack.