Three others who sustained injuries in the incident were admitted to hospital.
"Five persons who had sustained severe burn injuries have died. A magisterial inquiry has been ordered in the incident," district collector P Narhari told PTI.
The deceased are yet to be identified, he said.
"The fire started from a cracker shop and quickly engulfed other shops located nearby," Indore Deputy Inspector General of Police, H C Mishra said.
The police promptly evacuated people from around the fire site located in a congested lane, he said, adding the blaze was put out after several hours of efforts by the fire brigade personnel.
According to eyewitnesses, 20 two-wheelers were gutted in the blaze.