The kidnapping took place on Tuesday when he was travelling from Lagos International airport to his residence in a high brow part of the city, it said.
The vehicle he was travelling in was ambushed by gunmen, with the driver sustaining injuries.
The High Commission said that efforts were being made to secure the release of the hostage whose name had not been revealed yet.
"The BHC is working closely with others to secure the release of the hostage. Because of the nature of this incident, the BHC is not going into further detail about it," it said.