Media in the DRC said the incident, in which a wildlife ranger was killed, happened near the city of Goma in Virunga National Park.
The national park borders Uganda to the east and Rwanda to the south, skirting Lake Edouard.
The FCO currently warns against all travel to the DRC’s eastern border, including North Kivu province where the incident took place, and all but essential travel to Goma.
It also warned its ability to offer consular assistance may be "severely limited".
It added that British government staff are not always in the area and the British embassy’s ability to offer consular assistance may be "severely limited".
Virunga is popular with tourists and is famed for its gorillas, but is currently disputed territory and subject to bouts of violence.
An FCO spokesperson said: “We are in close contact with the authorities in Democratic Republic of the Congo following an incident involving two British nationals, and our staff are providing support to their families.”