Finnish broadcaster YLE says 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.
Tabloid Ilta-Sanomat said six people were injured, one man and five women, and that a woman with a stroller was attacked by a man with a large knife. It is unclear which victim died.
Finnish police say they are looking for more potential suspects.
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