Shehu of the Badole Quarter, Dandume Local Government Area of the state, reportedly confessed to be responsible for the incident.
The police said the incident occurred on July 1, 2020.
The burnt house belonged to one Hajiya Alhakutu, who also sustained injuries in the incident.
The police gave the identities of the dead toddlers as one-year-old Maryam Mohammed and four-year-old Asabe Abdulbasir.
They were said to have sustained serious burns and died while receiving treatment at the General Hospital, Funtua.
The police said Shehu was arrested shortly after the incident and reportedly confessed during interrogation to have committed the crime.
Shehu was charged with culpable homicide and causing grievous bodily harm, contrary to sections 189 and 215 of the Katsina State Penal Code.