The incident happened in the town of Aba on Friday when suspected assailants burst the pipeline operated by the state-run Pipeline and Product Marketing Company.
"The incident occurred at about 1:30am (00:30 GMT). Those burned are more than 30 with many others sustaining injuries," Nnamdi Tochukwu, a survivor said on Saturday.
A security officer, who did not want to be identified, confirmed the death toll.
"Over 30 bodies were burned at the scene before the arrival of security operatives while many others are currently receiving medical attention at various hospitals within and outside the town," the officer said.
A spokesperson for the state-run Nigerian National Petroleum Corporation (NNPC) said the victims were vandals attempting to scoop petrol from the pipeline.
"I can't give the exact number of casualties for now, but the explosion was caused as a result of oil thieves who had hacked the line to intercept the flow of petrol from the Port Harcourt refinery to Aba," Ndu Ughamadu told AFP news agency.
He said an investigation was under way.
Nigeria, Africa's largest oil producer and exporter, runs a network of pipelines that transport crude and petrol across the vast nation.
Thieves often break into pipelines that sometimes explode as villagers scoop up fuel.
One explosion in 1998 in the Niger Delta killed more than 1,000 people.
At least 269 people died in a blaze in 2006 at a vandalised oil pipeline.