According to local security officials the kidnappers were members of the Bakeel tribe and not Islamic militants.
Gunmen stopped the British couple and a Dutch family on Sunday as they drove through a mountainous area in northern Yemen, known locally as "kidnap corridor", near the town of Hawf, about 140km(87 miles) north of the capital, Sanaa.
The kidnappers commandeered the foreigners' cars and drove them to Barat, about 13 miles further north.
In London, the Foreign Office identified the two British hostages as Eddie Rosser and his wife Mary, both in their 60s and from the south of England.
The Foreign Office said the couple worked for the Dutch aid organisation Worldwide Services and were travelling with the Dutch couple and their two sons, aged six and seven.
The Dutch Foreign Ministry has declined to identify the family, but said the Dutch couple also worked for Worldwide Services, which runs a health care project in Saadah, a town on the road they were travelling. A spokesman for the Dutch embassy in Yemen said the situation was complicated by Eid al-Fitr celebrations to mark the end of the Muslim fasting month of Ramadan.
Yemeni security officials said the government was negotiating for the hostages' release with elders of the Hashid tribe, which controls the region where the smaller Bakeel tribe lives. The Bakeel kidnappers are seeking the release of a tribesman who was detained in November in connection with a murder.
A spokesman for the Foreign Office has said the British and Dutch ambassadors are working with the Yemeni government to secure the hostages' freedom.
"Both the Yemeni Interior Minister, Hussein Arab, and the Yemeni Prime Minister have told [the British ambassador] that they fully accept the importance of not using force to secure the hostages' release," the spokesman said.
The Yemen hills are increasingly unpredictable and dangerous. It is the third time in less than a month that Britons have been kidnapped in in the country.
The spokesman added: "We are, of course, urging the Yemeni authorities not to use force in order to secure the release of the hostages."
The kidnap does not appear to be related to the politically motivated seizure of 16 tourists in December, which resulted in the shooting dead of three Britons and an Australian, but is rather the latest in a wider series of kidnappings in which tribesmen have abducted Westerners for ransom. It is rare for hostages to be hurt during such abductions.
More than 150 foreign residents and tourists have been kidnapped by local tribesmen in Yemen in the past five years.
The rising level of tension in Yemen has prompted the British embassy to write to all UK citizens there urging them to consider whether their presence is essential. The families of several diplomats and expatriate workers have already left the country.
A British oilman, John Brooke, was released last week after five days as a hostage in Yemen after a secret deal between Yemeni security forces and kidnappers from the Al-Juayd tribe.Reuse content