The fire broke out at 09:30 local time in Seme-Podji municipality, near the border with Nigeria.
"The fire burned down the store and according to an initial assessment resulted in 35 deaths including one child," said Prosecutor Abdoubaki Adam-Bongle in a ministry statement, adding that an investigation had been opened to determine the cause.
More than a dozen others were seriously injured and are being treated in hospital, he said.