The Finnish newspaper Helsingin Sanomat reported that eight people had been taken to the hospital following the stabbings, some of whom were in critical condition. The attack was reported from the southwestern city of Turku, where police reportedly shot a man in the leg before arresting him in this connection.
Security forces tweeted that police were "looking for other possible perpetrators".
A tweet from South-West Finland police at 16.40 read, "Several people stabbed in central Turku". Majority are women, including one with a stroller who was attacked by a man with a large knife. The Islamic State group has claimed responsibility for the Barcelona attack.
Police have confirmed "several people have been knifed" in the centre of Turku this afternoon - including "a woman and a baby". They also reinforced security in Helsinki airport and streets as well as a train station in Vantaa.
Kolehmainen said it was "nothing is known about the motives. or what precisely has happened in Turku".
Police said that the incident was not being investigated as a terror attack, but that could change as new information comes to light. Hours later, terrorists launched a second attack in the seaside town of Cambrils, injuring seven people, one of whom later died.More news: Floyd Mayweather Conference Call Today At 6 PM ET
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"We heard a young woman screaming", Laura Laine said.
The attacker has been taken into custody.
Interior Minister Paula Risikko said: "We have not been able to confirm the person's identity. we have been in contact with the immigration service as the person looks like a foreigner".
In 2012, Finland s then-prime minister Jyrki Katainen escaped a knife attack in Turku while campaigning for municipal elections.
Turku lies on Finland's southwest coast about 160 km (100 miles) west of the capital Helsinki.
Police urged people to keep clear of the city centre while officers searched for other perpetrators.