The promotion, launched yesterday, reduced the price of more than a million 950-gram jars from 4.70 euros ($5.85) to 1.41 ($1.75).
In one video posted on Twitter, customers are seen shoving each other and shouting as they try to get as many jars as possible.
According to Le Parisien newspaper, shoppers started to fight in the northern town of Ostricourt, prompting police to step in.Intermarche did not immediately answer a message from The Associated Press seeking comments.
Ferrero, the company that produces Nutella, decried the incidents and distanced itself from the supermarket chain."We want to clarify that the decision for the special offer was taken unilaterally by Intermarche," the company said in a statement.
"We regret the consequences of this operation, which created confusion and disappointment in the consumers' minds."The discount was meant to last until Saturday but stocks ran out very quickly at many supermarkets. Sales went smoothly in some places, however, with no incidents reported in several supermarkets taking part in the promotion.