A local tabloid, Ilta-Sanomat, reported that one man and five women were injured.
Armed police scrambled to the middle of Turku as a knife-wielding group reportedly rampaged through the city.
On Twitter, police urged people to avoid that part of Turku.
Eyewitnesses report hearing one or more gunshots, and seeing at least one person lying, apparently lifeless at Puutori.
They added that they were looking for more potential suspects over the attack.
The suspect has been shot in the leg and brought into custody.
The man reportedly went on the rampage in the western city of Turku at around 4.30pm local time (2.30pm United Kingdom time).
Finnish Police have also reinforced security and Helsinki Airport and train stations following the stabbing incident.