An Ethiopian government source told the AFP news agency; "The army is dealing with the search. Troops have been deployed in the region."
Ethiopia's state news agency reported police as saying the Britons were taken from from a camp on Thursday night.
Britain has sent a team of officials to Ethiopia to help the search.
"We're sending out staff to supplement the embassy staff there," a foreign office spokeswoman in London told AFP.
French embassy officials have also travelled to the region in an attempt to help trace at least seven French nationals who were reportedly part of a trekking group.
The missing Ethiopians were working as drivers and interpreters for the tour groups.
The government requires all convoys visiting the area to have a minimum of two cars and travel with armed guards because of the threat of bandits.
"We heard about an abduction and we are trying to confirm their whereabouts," Berekhat Simon, an adviser to Meles Zenawi, the Ethiopian prime minister, told AFP.
"We'll try our best to ensure their safety."
In 1995, nine Italian tourists were captured by Afar tribesmen, then released two weeks later.
Afar separatists began a low-level rebellion against the Addis Ababa government in the 1990s, calling for the creation of a separate Afar state on territory which straddles Ethiopia, Eritrea and Djibouti.