Finnish broadcaster YLE says several people were seen lying on the ground in Puutori square in central Turku. On Twitter, police urged people to avoid that part of Turku.
One person has been "apprehended," Finnish police said, adding "several people had been stabbed." Their conditions weren't immediately available.
Tabloid Ilta-Sanomat says six people were injured, one man and five women, and that a woman with stroller was attacked by a man with a large knife.
Prime Minister Juha Sipila said the government was closely monitoring the ongoing police operation and holding an emergency meeting later Friday.