The horrific attack took place at around 9.45am on Tuesday at the Casino supermarket in the town of La Ricamarie, near Saint-Etienne, in central France.
According to reports on French TV TF1 the attacker walked up to the woman, pulled out a knife and cut her throat.
“She died at the scene whilst being treated by first aid teams,” said prosecutor Jean-Daniel Regnauld.
According to police the attacker is still at large. The supermarket remained closed following the attack.
According to early reports the victim was a member of a local travelling community.