They added that they were looking for more potential suspects over the attack.
Eyewitnesses report that several people were lying on the ground at the city's Central Market Square and about two blocks away at the Puutori-Market Square area.
One person was arrested Friday after several people were stabbed in the Finnish city of Turku, the Reuters news agency reports.More news: Angelo State Previews Solar Eclipse Event
According to The Sun, one person, presumably one of the attackers, has been shot by police.
A number of people were reportedly seen running with knives in the city centre of Turku, on the southwest coast of Finland.
A few minutes later police tweeted that they had shot a suspected assailant in the leg and taken him into custody.
Finnish police patrol on motorbike after stabbings in Turku, in Central Helsinki, Finland, Aug. 18, 2017.