Prosecutors said the store in the southern Paris suburb of Creteil had caught fire overnight, days after it was hit by anti-Semitic graffiti.
"The damage is believed to be very severe," Creteil prosecutor Laure Beccuau told French news agency AFP, adding that investigators do not believe the fire was accidental.
The Promo & Destock store was one of two neighbouring kosher shops in Creteil that were daubed with swastikas last Wednesday.
The fire comes on the third anniversary of the attack on January 9, 2015, at a kosher supermarket in northern Paris by jihadist gunman Amedy Coulibaly, who killed three customers and a Jewish employee.
That attack came two days after Said and Cherif Kouachi -- close friends of Coulibaly's -- gunned down 11 people at the offices of satirical magazine Charlie Hebdo, the first of a wave of jihadist attacks in France over the past three years.
The 2015 attack on the Hyper Cacher supermarket triggered deep concern among France's large Jewish community over growing anti-Semitism.
A record 7,900 French Jews emigrated to Israel in 2015, though the exodus has since slowed.
Former prime minister Manuel Valls told Europe 1 radio on Wednesday that more needed to be done to tackle anti-Semitism, which he said had become "deeply rooted" in France.
"What has changed over the past three years is the awareness of this level of anti-Semitism," he said.
Valls added that French society as a whole had failed to mobilise in support of Jews following anti-Semitic attacks such as the 2012 Islamist shooting at a Jewish school in Toulouse in which four people were killed, including three children.
"These are crimes that must be prosecuted and condemned, we need to do more," he said.