A woman shouting "Allahu akbar" – "Allah is great" in Arabic – wounded two people with a box cutter Sunday at a supermarket in southern France before she was arrested.
A store customer in the maritime town of La Seyne-sur-Mer was slashed in the chest and hospitalized. A cashier was also injured but hurt less seriously, French radio station Europe 1 reported.
Prosecutor Bernard Marchal said the suspect may have mental health problems. She has not been identified.
"It's apparently an isolated case involving a person with psychiatric issues," the prosecutor told Le Monde newspaper. "However, that does not exclude the possibility that the suspect was radicalized," Marchal added.
"There is a presumption of attempted murder and ... of a crime with terrorist implications," Marchal told the newspaper.
The regional newspaper Nice-Matin, which first reported the 10:30 a.m. attack Sunday, quoted an unidentified witness who said other customers in the store stopped the woman from cutting anyone else.
France remains on edge since an attack and hostage-taking incident in a supermarket near the southern French town of Carcassonne left four people dead in March.
A man also attacked people near the Paris Opera House in May, killing one person and injuring four, an action claimed by the Islamic State.
Last week, a man who took hostages in a Paris building was hospitalized in a psychiatric unit.
Adding to concerns are the hundreds of French ciizens who have traveled to the Iraq-Syria war zone and are returning as IS crumbles.