The Foreign Office in London said it had received reports the Islamist militants were "actively planning" to seize foreign workers in the Bama local government area of Borno state.
Both said in travel advice that the affected area was "along the Banki-Kumshe axis", which is near the border with Cameroon.
The US embassy in Abuja said in a message to its nationals that the report was "credible".
Boko Haram has kidnapped thousands of women and children, including more than 200 schoolgirls from the Borno town of Chibok in 2014, which brought the conflict to world attention.
At least 20,000 people have been killed since 2009. But abductions of foreigners have been rare.
There was a spate of kidnappings of foreign workers in the wider north from 2011 to 2013, claimed by a Boko Haram splinter group, Ansaru, which was more ideologically aligned to Al-Qaeda.
The leader of Ansaru, Khalid al-Barnawi, has been charged with the abduction and murder of foreign workers, among them an Italian, a Briton, a German, Greek, Lebanese and Syrians.
Most were engineers or construction workers.
International aid workers now account for the majority of foreign nationals in northeast Nigeria. Most are based in the Borno state capital, Maiduguri.
Hundreds of thousands of people in the Lake Chad region require urgent food aid as a result of the conflict, which has made more than 2.6 million people homeless and ravaged farmland.
AFP visited Banki with other international media two weeks ago.
Humanitarian agencies operating in the town include the World Food Programme, International Organization for Migration and other UN bodies.
Banki was liberated from Boko Haram in September 2015 and is currently home to some 32,000 displaced people in a sprawling, overcrowded camp.
The surrounding area still suffers from frequent Boko Haram attacks on military convoys, as well as suicide bombings.
Fighters loyal to Boko Haram leader Abubakar Shekau, who were pushed out of their camps in the Sambisa Forest area last December, are believed to be responsible.
The kidnap warning and the threat to humanitarian operations underlines the fragility of security in northeast Nigeria, despite claims from the government and military that Boko Haram is a spent force.
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