The three shots were fired in the midst of the evening rush in central Tampere. A woman, who was accompanied by a child, was hit and has died.
The child was not physically injured in the shooting, according to Finnish media.
The man suspected of having fired the shots fled the scene but was apprehended during the night. A few hours later, it was announced that the woman had died from her injuries.
The incident is now being investigated as murder and illegal possession of firearms, as well as reckless endangerment, according to Finnish media.
The victim and the perpetrator knew each other previously, reports the public service channel Yle's Swedish-language service.
