The suspect, a Syrian refugee born in 1991, is under formal investigation for attempted murder and resisting arrest with a weapon, the prosecutor said.
The injured are no longer in critical condition, Annecy Prosecutor Lise Bonnet-Mathis told a news conference, adding that the four children were still hospitalised.
The suspect has chosen not to speak while in police custody and when presented before judges, she said.
He was examined by a psychiatrist who considered that his state of health was compatible with him being held in custody.
"Presently it is premature to assess his motivations," Bonnet-Mathis said, reiterating that there was no indication yet that terrorism was the assailant's motivation.
(Reporting by Dominique Vidalon, Cecile Mantovani; Editing by Hugh Lawson)
