Police had yet to confirm how many people had been wounded but witnesses said they had seen several bodies lying on the ground in a busy area of the southwestern city.
Police shot one suspect in the legs and arrested him, while security forces wrote on Twitter that police were "looking for other possible perpetrators".
"They ask the population to leave and avoid central Turku," the tweet added.
Public television station Yle reported that central Turku was on lockdown, with businesses shut.
The stabbing spree comes with Europe on high alert a day after drivers slammed into pedestrians in twin attacks in Spain, killing at least 14 people and injuring more than 100 others. The Islamic State group has claimed responsibility for the Barcelona attack.
"The government is following the situation in Turku closely and a police operation is under way," tweeted Prime Minister Juha Sippila ahead of a cabinet meeting.
In 2012, Finland's then-prime minister Jyrki Katainen escaped a knife attack in Turku while campaigning for municipal elections.
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