The blast also caused damage to several cars and a telephone box, while windows were smashed in nearby properties.
Police in the city said it was unclear what had caused the explosion, which took place at around 3.30am in the suburb of Södra Sofielund, close to the city centre and one of the biggest medical hubs in the region, Skåne University Hospital.
The blast followed a brawl in the neighbourhood, with witnesses reporting between ten and 20 people rowing on the street on Thursday evening.
However it is understood that the two men injured in the blast were not linked to the earlier row.
One was delivering newspapers and the other happened to be walking in the area, police told the TT news agency. Neither casualty is understood to have been seriously hurt.
Malmö has experienced growing violence in recent years. Its outer suburbs have a reputation for gun and gang-related crimes as well as race-related violence between different immigrant groups.
On Tuesday, police arrested more than two dozen suspects after gunfire rang out in the Rosengård area in what officers said was an attempted murder.
In February, a car blast in the city centre shattered several windows at Malmö's Museum of Modern Art.
And back in December, a series of explosions damaged buildings in the east of the city.