“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 the police operation focusing on a busy square. Businesses were shut.
MTV3 television reported that police have increased security at Helsinki airport and at train stations.
The stabbing spree comes with Europe on high alert a day after drivers slammed vehicles into pedestrians in two 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 motive for the stabbing in Turku was not yet known. Finland’s interior minister was due to give a press conference at 1600 GMT.
“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.
The man who approached him carrying a knife was found to be psychologically disturbed and no charges were brought against him.
A former capital of Finland, Turku remains a hub for business and culture.