Huda's brother-in-law Akram Uddin lodged the case on Wednesday, said Faridpur Kotwali police OC Md Nazim Uddin.
The 48-year-old's teenage son is the sole accused in the case, he added.
He said legal steps against the son were underway.
Rafiqul Huda, who hails from Faridpur, is the brother of former chief election commissioner ATM Shamsul Huda.
Huda and his wife were rushed to Faridpur Medical College Hospital, but he was transferred to Dhaka the same day as his condition deteriorated.
He succumbed to his injuries Wednesday morning at Dhaka Medical College Hospital's burns unit.
The unit's Resident Doctor Partha Shankar Pal said he had sustained 95 percent burns.