Witnesses reported seeing the attackers fleeing on bicycles after the shooting took place at about 9pm on Saturday.
Just moments earlier, a bomb placed under a car was detonated in another part of the city, destroying the vehicle and damaging others, although there were no reports of injuries.
Police in Sweden said it could not yet say whether the two incidents were linked and did not identify suspects in either case.
Jacob Bjorkander told Swedish newspaper Sydsvenskan that he had been cycling near the pizza restaurant with his two young children the night of the shooting.
He said: “It’s regrettable, absolutely awful, and lacking in any respect.
“This should be the end of it. It’s gone too far. People should be out on the streets showing what they think, that we don’t want this in our town.”
Explosions and shootings in the past few years in Malmo, Sweden’s third-largest city, have been linked mainly to organised crime and feuding gangs.
However, Swedish news agency TT said five fatal shootings and 29 explosions, including Saturday’s incidents, have taken place in Malmo this year - figures substantially lower than during all of 2018, according to police statistics.
Katrin Stjernfeldt Jammeh, chairwoman of the local municipality council, told Swedish broadcaster SVT she was concerned Saturday’s events would escalate the spiral of violence seen in past years in Malmo, a city of some 320,000 residents.
She said: “It is every parent’s nightmare to lose a child. It’s been a heavy and black night in Malmo.
“We’ve been in this situation before with similar events. This is what the police have warned about, namely an escalation of cruel and reckless violence in Malmo.”
Ulf Kristersson, leader of the centre-right opposition Moderate Party, urged Social Democrat prime minister Stefan Lofven to act quickly to curb the violence.
Additional reporting by Associated Press
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