Authorities will look into if the 70% discount deal at a French supermarket, that last week caused violent scenes, broke trading laws.
The country's laws are strict concerning discounts outside biannual sale periods.
Customers at Intermarché shops pushed each other over heavily discounted Nutella, with the police eventually being called.
Of the brawls, a witness told French media: "They fought like animals. A woman had her hair pulled, an elderly lady had a cardboard box put on her head, another had a bloody hand, it was terrible."
Consumer watchdogs in France want to find out if the price cut on 950g jars of Nutella from €4.50 to €1.40 fell within the January sale window, when large discounts are allowed.
If it turns out the reduction fell outside this period, which runs for six weeks from the second Wednesday of January, the chain may have breached regulation concerning "unfair competition".
"Traders may offer promotions throughout the year with a reduction in prices," trade laws stipulate, provided "they do not sell at a loss".
Authorities will seek to discover how much Intermarché paid for the jars of Nutella.
The regulation also applies to online shops but dates for border towns and French overseas territories are more flexible.
Stéphane Travert, the minister of agriculture for France, devised plans before the Nutella hysteria that will pass before the country's Assemblée Nationale on Wednesday.
He wants to limit discounts to 34 per cent of the sum a shop originally paid for a product and put a stop to buy-one-get-one-free offers
International news website The Local France on Wednesday also reported a "nappy rush" at an Intermarché supermarket in the northeastern French city of Metz.
It said the supermarket chain was offering a promotion for a “mega pack” of Pampers nappies for €7.18 rather the usual €23.95—a discount of 70%—which sparked similar scenes to the Nutella "riots".
“It was horrible. It was out of control. Around 250 people were there when the shop opened, just to buy the nappies. Women were fighting each other,” the store's manager told the Republicain Lorraine newspaper.