The house served as Obasanjo’s Abeokuta residence when he was president between 1999 and 2007.
Reports said the fire which started at about 10 p.m. on Wednesday was instigated by a power surge.
The Ogun State Director of Fire Service, Fatai Adefala, confirmed the incident to reporters but did not state the level of damage caused by the fire.
Men of the state fire service were said to have put off the fire with the help of sympathizers and domestic workers in the house.