"Our priority is securing the earliest release of the eleven crew who have been taken and we are working closely with our partners and the local authorities to achieve that," Midocean said.
"The families of those crew members taken are being kept informed of the situation," said the company. It added the vessel had proceeded to safe waters.
Midocean declined to say where the kidnapped crew members were from but Polish state media, citing foreign minister Jacek Czaputowicz, said eight of them were from Poland.
The nationality of the three other abducted crew members was not immediately clear.
Kidnappings and piracy in Nigeria and the Gulf of Guinea are common.