Police said on Twitter a man suspected of being the attacker was shot in the leg and arrested.
They said were looking for more potential suspects involved in the attack which took place in the early afternoon in the south-western coastal city.
Finnish broadcaster YLE reported that several people were lying on the ground in the centre of the city.
A local tabloid, Ilta-Sanomat, reported that one man and five women were injured.
It claimed that a woman with a pushchair had been attacked by a man with a large knife.