Update 9.15pm: Police said the man in custody is likely to have acted alone, but they are not ruling out the involvement of other people.
They said the man stabbed eight people, killing two of them, before police shot him in the thigh and detained him. Authorities are trying to determine his identity and nationality.
The country's president, Sauli Niinisto, visited Turku later Friday and condemned what he called a "shocking and cowardly act".
He said officials are doing what they can "so that all Finns are able to feel safe".
Update 5.15pm: Two people have been killed and six others were injured in a stabbing incident in the western Finnish city of Turku, police said.
A suspect is in custody and being treated in hospital after officers shot him.
Turku is about 90 miles west of the capital, Helsinki.
Security is being stepped up across the country in the wake of the incident, Finland's interior minister Paula Risikko said during a news conference.
Syvä osanottoni Turun uhreille ja heidän läheisilleen. Poliisiylijohtajan kanssa matkalla Turkuun. #Turku— Paula Risikko (@paularisikko) August 18, 2017
Update 5pm: One person has died in the stabbing incident in western Finland, according to reports.
Earlier Police in Finland have shot a man in the leg after he was suspected of stabbing several people in the western city of Turku.
Broadcaster YLE said several people were seen lying on the ground in the central part of the city.
On Twitter, police urged people to avoid that part of Turku.
Several persons stabbed in central Turku. Police has shot at suspected perpetrator. One person is apprehendee— L-S poliisi (@L_S_poliisi) August 18, 2017
The police is searching for possible more perpetrators in Turku. People are asked to leave and avoid the center of Turku.— L-S poliisi (@L_S_poliisi) August 18, 2017
One person has been "apprehended," Finnish police said, adding "several people had been stabbed".
The victims' conditions have not been revealed.
The tabloid Ilta-Sanomat said six people were injured, one man and five women, and that a woman with a buggy was attacked by a man with a large knife.
A search for potential suspects is ongoing.
Persons who have information regarding happenings in Turku, can call the numbers +358 503499187 or +358 50 3268089— L-S poliisi (@L_S_poliisi) August 18, 2017
The Irish embassy in Finland say there are no reports of Irish people being caught up in the incident.
Anyone with concerns is being advised to call the Department of Foreign Affairs in Dublin.
Prime minister Juha Sipila said the government is closely monitoring the ongoing police operation and will hold an emergency meeting later.
A news conference is planned for 7pm local time (5pm Irish time) in Turku.