The deceased identified as Fatema Begum, 27, and her daughter Marjan, 3, hailed from Lakshmipur.
Fire service sources said the fire originated from an electric short circuit around 3:30am.
On receiving information, nine fire fighting vehicles of three units rushed to the spot and doused the fire after five hours' frantic effort.
Jashim Uddin, deputy assistant director of Fire Service, Chittagong told the Dhaka Tribune that the mother and her daughter had died on the spot when the fire engulfed the slum located beside rail tracks near EPZ.
“The bodies of the ill-fated victims were recovered soon after the blazing fire was put out,” said the official, adding that a total of 12 shops and 10 shantis were gutted in the fire.