After the first tank caught fire late Friday, the blaze spread to a second tank by the early hours of Saturday.
The first two tanks collapsed overnight Sunday, causing three more reported injuries and spilling their oil.
According to the Cupet state oil company, the first tank had contained about 26,000 cubic meters of crude, about half its capacity.
The second contained 52,000 cubic meters of fuel oil. It was not immediately clear how full the third tank -- also with a capacity of 52,000 cubic meters -- was.
Firefighters had been battling to prevent the third tank from catching fire, dousing it with water to keep it cool, but ultimately to no avail.
The depot, built in the 1980s and modernized several times, supplies the Antonio Guiteras thermoelectric plant, the largest in the communist nation.