The vehicle crashed in the Odukpani area of the southeastern state of Cross River, just north of the state capital, Calabar, at about 5pm (1600 GMT) on Friday.
Local residents rushed to collect the leaking fuel when it caught fire, triggering the blast.
Cross River state police spokeswoman Irene Ugbo said the blast could have been sparked by the clashing of steel containers used to scoop up the petrol.
"I can't confirm the exact number of casualties," she said, adding: "The casualties are high."
The injured were taken to the University of Calabar Teaching Hospital for treatment to varying degrees of burns.
One local resident, Akpan Imon, said at least 18 people were killed.
"I counted 18 bodies including women and children burnt beyond recognition," he said.
"I believe the casualty level could be more because people from other neighbouring communities had thronged the scene."
Another local, Sunday Ibor, said "over 20 bodies" were taken to the local government secretariat.
Petrol tanker and pipeline blasts are common in Nigeria, where despite the country's multi-billion-dollar oil and gas industry, most people live in poverty.
Fires and explosions often occur as people try to siphon fuel from pipelines and also following accidents involving fuel tankers on badly maintained road.
In July 2012, at least 104 people were killed and some 50 others wounded as they tried to collect fuel from a petrol tanker after an accident in the southern state of Rivers.
Most were killed in the subsequent fire.
In June last year, at least nine people died in Nigeria's commercial capital, Lagos, when a petrol tanker crashed, triggering a wildfire that gutted more than 50 vehicles.
Published : January 12, 2019
By : Agence France-Presse Warri, Nigeria