The fire broke out last night and at least 12 shops were gutted.
The fire, suspected to be caused by a short circuit, was controlled after six hours this morning.
Around 1.50 lakh litres of water and 300 litres of chemical were used to douse the fire, fire officer Rakesh Vyas said.
District Collector Rohit Gupta, Kota city S.P. Anshuman Bhomia and other officials rushed to the spot and carried out rescue and fire control operations.
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Six other injured have been admitted to a hospital.
As the fish market was located in a congested area, firemen found it difficult to control the blaze.
The bodies were handed over to the family members after postmortem.