President Muhammadu Buhari described the incident in Imo state, southern Nigeria, as a "catastrophe and a national disaster".
Many victims were burnt beyond recognition.
The police are now looking for the owner of the illegal refinery.
The damage to fishing and farming caused by the oil industry over the decades and the failure to share the oil wealth has led some to find other ways to make money.
Illegal refining is attractive as in parts of the oil-rich Niger Delta it is seen as being relatively easy to pull off, despite efforts to halt the practice.