The Turun Sanomat newspaper reported that police were inspecting departing trains and buses and reinforcing security in the capital of Helsinki, adding that a suspect is in custody and being treated in a hospital after officers shot him in the thigh.
Police in Finland said they have arrested one suspect and are looking for more potential suspects in the stabbing of several people in the western city of Turku. In a video of the attack, the stabber can be heard yelling "Allahu Akbar."
Police made the announcement on Twitter, also warning people to leave and avoid central Turku.
Finnish broadcaster YLE said several people were seen lying on the ground in the central part of the city.
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.
Following the attack, Finland's interior minister said security is being stepped up across the Nordic country after stabbings that killed at least two people in a western city.
Minister Paula Risikko made the announcement during a news conference in Turku, where the stabbings happened.
An eyewitness saw four or five ambulances near the city's main square, the paper said.
"The government is closely following the events in Turku and the ongoing police operation. The government will meet later today," Prime Minister Juha Sipila wrote on his Twitter account.