"There are eight victims in the stabbing. Two dead and six injured," Turku police tweeted today after the assault in a market square.
Police shot one suspect in the legs and arrested him. Security forces wrote on Twitter that police were "looking for other possible perpetrators".
"They ask the population to leave and avoid central Turku," the tweet added.
The motive of the suspect or suspects was not immediately known.
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In Turku, images of a body covered in a white blanket at the scene of the stabbing was published on some online news sites, including the local daily Turun Sanomat.
The attack took place in the heart of the port city in southwestern Finland, just after 3:00 pm (1300 GMT) in a bustling neighbourhood.
"I saw an old woman, I tried to help her. She was bleeding all over her body," Wali Hashi, who witnessed the attack, told AFP.
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. We saw a man on the square, with a knife in his hand and he was waving it."
Central Turku -- located about 140 kilometres (90 miles) from the capital Helsinki -- was swiftly cordoned off and stores and restaurants closed.
Police also tweeted that they had raised their emergency readiness nationwide, increasing security at airports and train stations.
"The number of patrols is being increased, information gathering is intensified," they wrote.
Police have refused to comment on whether the stabbing may have been terrorism-related.
In June, Finland's intelligence and security agency Supo raised the country's terror threat level by a notch, from "low" to "elevated", the second notch on a new four-tier scale.
"Supo has become aware of more serious terrorism-related projects and plans in Finland," it said.
"Foreign terrorist fighters (who have) left from Finland have gained significant positions within IS in particular and have an extensive network of relations in the organisation," it said in its June assessment.
The man who approached him carrying a knife was found to be psychologically disturbed and no charges were brought against him.
In late 2016, a local politician and two journalists were shot dead in a Finnish town close to the Russian border, illustrating Finland's struggles to combat gun crime.
Police had quickly arrested a man singled out by witnesses as the killer.
A former capital of Finland, Turku remains a hub for business and culture.