The new Foreign Secretary continued to Brussels by other means.
The unplanned stop also caused disruptions to other flights leaving the airport and people quickly took to social media to vent their frustration.
One Twitter user wrote: "Short delay for Boris... In the meantime, flights cancelled for everyone else! Yay Boris!", while another said: "So my flight back to London is delayed thanks to Boris Johnson. Great."
Others took the opportunity to poke fun at the new Foreign Secretary, with one Twitter user writing: "Presumably he tried to take back control of it for reasons of personal ambition?"
While another said: "The Foreign Sec who can't even leave the country!" and a third wrote: "Even aircraft know that Boris Johnson travelling abroad on behalf of the country is not a good idea."
A spokesman for Luton Airport said: "At 5.26pm an RAF aircraft landed safely at London Luton Airport after reporting a technical issue.
"Emergency procedures were put in place and all 16 passengers left the aircraft safely. Several scheduled flights were disrupted whilst the runway was cleared. The runway reopened at 5.59pm."
Johnson, who helped lead the campaign for Britain to leave the European Union, was appointed Foreign Secretary by new Prime Minister Theresa May on Wednesday.
His appointment triggered near uproar in European capitals, and he was booed at the French ambassador's Bastille Day party in London.
The event on Thursday was his first engagement in the role.
Johnson later had to respond to the Nice terror attack and the failed coup attempt in Turkey in an eventful first week.
EU foreign affairs chief Federica Mogherini was due to welcome the former mayor of London on Sunday 'for an initial contact' before he sets about rebuilding relationships with his counterparts during meetings on Monday.
He will meet EU officials in Brussels for the first time since the referendum result.