The store was one of two Paris kosher shops to be daubed with swastikas last week, prompting fears of rising anti-Semitism.
The grocery store, which is located in the southern Paris suburb of Créteil, was set on fire in the early hours of Tuesday morning, at around 5am, local prosecutor Laure Beccuau told the AFP news agency.
Mrs Beccuau said that the building had suffered “heavy fire damage,” adding that while it was still “too soon” to discuss motives, investigators did not believe the fire was an accident.
An investigation has been launched into the suspected arson attack.
Mrs Beccuau’s office said: “The store’s metal shutter was found lifted, and the fire is thought to have started somewhere along the aisles.”
The store has been completely gutted and the aisles are blackened and charred, according to AFP.
Run by a Muslim, the Promo & Destock store was one of two adjacent stores in Créteil to be daubed in red swastikas last Wednesday.
The neighbouring store that was vandalised with anti-Semitic graffiti – l’Hypercacher – was also damaged in the fire.
Aliza Bin Noun, Israel’s ambassador to France, said the fire was a “shameful provocation” on the third anniversary of the January 9, 2015 attack on the Hyper Casher kosher supermarket in eastern Paris.
Islamist State gunman Amedy Coulibaly killed three shoppers and one of the store’s employees two days after his accomplices, brothers Chérif and Saïd Kouachi, killed 12 people at the Paris offices of the satirical weekly Charlie Hebdo, triggering a wave of deadly terrorist attacks in France and sparking anti-Semitism fears nationwide.
Some 23,000 Jews live in Créteil, a town of 90,000 inhabitants, community leader Albert Elharrar told AFP, adding there was a “link between the graffiti and the fire” and that the shops had been “deliberately targeted” on the anniversary of the 2015 attack.
A second religious hate crime was reported in the central French town of Châteauneuf-sur-Cher on Tuesday.
A “heavily intoxicated” man was caught by a worshipper daubing swastikas on the wall of a Muslim prayer hall, local officials said, adding that the man had been arrested and placed in a drunk tank.
According to France Inter radio, the Châteauneuf-sur-Cher mosque is known to French intelligence services as a hotbed of Salafist activity.