A photographer working for Reuters news agency said he counted about 500 corpses, many burnt beyond recognition.
Hundreds of people went to scoop fuel from the pipeline after thieves punctured it overnight at Abule Egba, a heavily populated area, Orebiyi said.
Speaking to Al Jazeera, Stella Din, a journalist at the scene, said that local officials and Red Cross workers were preparing a mass burial site to accommodate more than 1,000 bodies.
"Residents woke up this morning to a massive inferno and saw hundreds of bodies," she said.
Local television stations ran messages advising residents living in neighbourhood close to the blast to leave.
Those who were burned were taken to hospital in Ikeja, another northern suburb.
Explosions at oil pipelines, often causing large numbers of casualties, are not uncommon in oil-rich Nigeria.
In October 1998, a pipeline explosion killed 1,082 people and injured hundreds more at Jesse in the Niger Delta, and 300 were killed in July 2000 in the same area.