STORY: The children wounded in the attack were aged between 22 months and three years. Two of the wounded children and one adult were in hospital in a life-threatening condition, while the other victims were less seriously hurt.
Le Paquier park where the attack took place is popular with local people and tourists who swarm to Annecy in summer to boat on the lake's turquoise waters and hike in the nearby forested mountains.
At least one of the wounded children was in a stroller, eyewitnesses said. One person who saw the attack, who gave his name as Ferdinand, told BFM TV: "(He) went towards the strollers, repeatedly hitting the little ones with a knife."
The suspect was a 31-year-old Syrian refugee granted asylum in Sweden 10 years ago and in France legally, Prime Minister Elisabeth Borne said.
Interior Minister Gerald Darmanin said France had rejected an asylum request made by the suspect earlier this month, and that he had been carrying "certain Christian religious insignia".
The local prosecutor leading the investigation said there was no indication that terrorism was the assailant's motivation. The suspect was under investigation for attempted murder.