The Movement for the Emancipation of the Niger Delta (MEND) said in an email sent to journalists they had detonated 30kg of dynamite using a mobile phone in the attack on Saturday.
"Our operatives in Delta state in the Niger Delta planted and detonated one car bomb amidst petroleum product bridging tankers located close to the refinery in Warri," MEND said.
The militants said the attack was similar to one they carried out at an army barracks in Port Harcourt on April 20 that killed two people.
Sunny Areh, a spokesman for the Delta State government, confirmed the attack.
He said a Mercedes 190 car had been packed with explosives and that the blast had destroyed four nearby parked cars but caused no casualties.
Brigadier General Alfred Ilogho, commander of a military task force deployed in the delta to counter the rebels, said that a car had exploded close to parked tanker lorries on the outskirts of the oil port of Warri.
"There was an explosion of a car. There weren't any casualties. The place has been cordoned off by soldiers," he said, adding that the blast had happened after dark at a truck stop used by tanker drivers serving Warri's refinery.
"We wish to warn the Chinese government and its oil companies to steer well clear of the Niger Delta"
The Movement for the Emancipation of the Niger Delta
MEND said the attack was a warning to all people working in Nigeria's oil industry.
"This is the last warning to all oil industry workers. This warning goes particularly to tanker drivers and all involved in the petroleum industry in one way or the other," MEND said in a statement.
The militants issued a specific threat to Chinese oil workers, warning Beijing not to invest in the Nigerian oil industry.
Hu Jintao, the Chinese president, earlier this week signed oil deals with Nigeria during a state visit.
"We wish to warn the Chinese government and its oil companies to steer well clear of the Niger Delta.
"Chinese citizens found in oil installations will be treated as thieves. The Chinese government, by investing in stolen, crude places its citizens in our line of fire," MEND said.