Police received a call just before 9.30pm about the stabbing, which occurred in the vicinity of a pedestrian tunnel near Agnesfridsvägen.
Witnesses on the scene helped the 22-year-old victim place a tourniquet on her wounds, the Sydsvenskan newspaper reported.
The woman was later taken to hospital for treatment of what were described as serious, but not life-threatening, wounds to her chest.
Several officers were dispatched to the scene of the attack and were able to arrest a 20-year-old man who had remained in the area.
While the man was initially arrested on suspicions of assault, the suspicions were later upgraded to attempted murder.
The attacker and the victim were reportedly acquainted with one another, but the exact nature of their relationship remains unclear.
“They don’t live together,” Malmö police spokesperson Bo Paulsson told the Expressen newspaper.
The infant in the pram at the time of the attack is being looked after by relatives of the victim and police are still working to determine a motive for the stabbing, pending the questioning of the involved.
“We haven’t been able to talk to him or her yet,” Paulsson added.