Gerald Darmanin said the attack took place in a square in the town of Annecy.
In a short tweet, he said police have detained the attacker.
“Several people including children have been injured by an individual armed with a knife in a square in Annecy,” he tweeted.
A local politician, Antoine Armand, tweeted that children were attacked on a playground.
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He called the attack “abominable”.
“We still know very little but all my support for the victims, relatives, law enforcement and rescue,” Armand said in a translation of the tweet.
In Paris, politicians interrupted a debate to hold a moment of silence for the victims, BFMTV reported.
Annecy is just over the border from Geneva in Switzerland, about 550km south-east of Paris.