Police shot the suspect in the leg and he was later taken to hospital. The attacker is being treated in hospital, with police being unable to question him yet.
Police raised an emergency readiness alert nationwide, increasing security at airports and train stations. People were allowed to return to the city centre a few hours later.
They later added: "The police is searching for possible more perpetrators in Turku".
Although the terrorists in Spain used cars - and may have had explosives they never managed to use against civilians - the incident in Turku, Finland was being reported as a knife attack, reported CNN.
Video shared online appeared to show people running away from danger, reportedly shouting warnings in Finnish.
A tweet from South-West Finland police at 16:40 local time (13:40 GMT) read: "Several people stabbed in central Turku". A lot of them are women, including one with a stroller who was attacked by a man with a large knife.
Rescue personnel have covered a stabbing victim's body at the Turku Market Square in the Finnish city of Turku where several people were stabbed on August 18, 2017.
Eyewitnesses described the panic at the scene. "I understood that he had stabbed someone".
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"We were just talking about what happened in Barcelona", he said.
Another witness, who did not want to give his name, told public television YLE: "A young woman screamed really loudly at one corner of the square".
The severity of injuries of other people involved in the attack is not now known.
Finland's Prime Minister Juha Sipila said his government was monitoring the situation closely. "The events of the day are shocking us all".
Stabbing attacks have taken place across Europe in recent months.
Turku has a population of more than 180,000 and is situated around 100 miles (166km) west of the capital Helsinki.
Anyone with concerns for loved ones in Turku can contact the department's consular assistance team on 00 353 1 4082000.