Over 36 people were inside the premises and several standing outside at the time of the incident.
"The fire broke out when people had queued up during the distribution of kerosene and food grain in Bargi in Harayi tehsil in the afternoon," Jabalpur Divisional Commissioner Gulshan Bamra told IANS.
Locals were buying ration during the Friday weekly market when the fire reached the kerosene drums stored in the shop for distribution and quickly spread to all directions, eyewitnesses said.
"So far, 14 bodies, three of them of women, have been recovered from the building," Chhindwara Superintendent of Police Gaurav Tiwari told the Press Trust of India. The cause of the fire is not yet known, he added.
Police and district administration officials rushed to the spot along with fire tenders and brought the fire under control.
Prime Minister Narendra Modi expressed shock over the incident. "My thoughts are with those who lost their loved ones in the fire at Chhindwara. The incident is shocking beyond words," he tweeted.
Madhya Pradesh Chief Minister Shivraj Singh Chouhan too expressed grief over the loss of lives in the mishap and announced an ex-gratia of Rs 4 lakh each to the kin of those killed and Rs 50,000 each to the injured.
A magisterial probe has been ordered into the incident.
(With Agency Inputs)