Finnish police shot the attacker in the foot and arrested him. The identity of the attacker, believed to be a foreigner, and the motive for the crime have not yet been determined.
Finnish authorities have warned people to stay away from the city and increase patrols and security across the country in case of many attackers. People were allowed to return to the city center a few hours later.
"At this stage, there is only one suspect and we are investigating whether there are many people involved... but it seems he alone committed the crime," said Mr. Markus Laine, an official with the Finnish national investigation agency.
"We are not investigating this as a terrorist attack, but the possibility has not been ruled out," he said.
Turku city residents have placed candles and flowers in memory of the victims at the site of the attack. Laura Laine, a witness to the stabbing, said: "First, we heard a young girl screaming. I thought it was just children playing around, but then I saw everyone starting to run around. And I saw a man holding a knife in his hand stabbing a woman."
"After that, a person ran towards us and screamed 'he has a knife' and everyone in the coffee shop ran inside," she recounted.
According to the police, 8 injured people were taken to the hospital.
Finnish Prime Minister Juha Sipila called the knife attack "a particularly serious act of violence in Finland".
Finland is a peaceful country, but since June, the country's Security Intelligence Service has raised the level of the terrorist threat when it detected that there were terrorist plans in Finland.
Before the knife attack in Finland, an attacker drove a truck into a crowd in Barcelona, Spain, running over, killing 13 people and injuring many others.
European Commission President Jean-Claude Juncker said: "I was very worried when I heard about the violent attack in Turku, Finland. We strongly condemn the unjust attack that occurred within 24 hours of the brutal attacks in Spain."
Two hours after the knife attack in Turku, Finland, another controversial knife attack killed a 31-year-old man and injured another 25-year-old man in the German city of Wuppertal. The incident occurred outside a hair salon near the city's central station. German police are searching for the perpetrator at buildings around the area.
