"The pirates ransacked the vessel for personal belongings and took five crew members with them on their departure," said spokesman Martin Baxendale. He later told AFP those taken were Indian nationals.
The statement said the remaining crew were safe and that the tanker had arrived at the port of Lagos, Nigeria's economic capital.
"Everything possible is being done to ensure the safe return of those crewmembers taken," it further said.
Armed gangs have frequently kidnapped expatriate oil workers in the Niger Delta, often demanding ransoms for their release.