The move highlights the widening gulf between London and the continent over how to respond to the new US president-elect after a senior German politician warned Theresa May was “delusional” if she believed the incoming Republican administration would give the UK a good trade deal.
Foreign Secretary Mr Johnson, who branded vocal European concern about the US election result as a “whinge-o-rama”, was dismissive of the need for a special EU meeting.
A Foreign Office spokesman said: “The Foreign Secretary will not attend the meeting convened for Sunday. There is a regular Foreign Affairs Council meeting on Monday where a range of issues can be discussed in the normal way.
“We do not see the need for an additional meeting on Sunday because the US election timetable is long established. An act of democracy has taken place, there is a transition period and we will work with the current and future administrations to ensure the best outcomes for Britain.”
The move came as a senior member of German chancellor Angela Merkel’s Social Democrat coalition partner, Axel Schafer, said the PM’s hope that President-elect Trump will look favourably on the UK will come to nothing.
Referring to the surprise election of Mr Trump, Mr Schafer told The Times: “What changed is the likelihood of a speedy and preferential trade deal between UK and US.
“Even before Tuesday the chances were rather low, now the hope for this kind of deal seems delusional.”
In further signs of tensions between the UK and EU, Czech state secretary for European affairs Tomas Prouza warned plans floated at the Tory conference to make companies list foreign workers were “stoking the fires” of anti-immigrant feeling in the UK.
Mr Prouza said the idea was similar to ones seen during the rise of fascism in the 1930s.
He called on Mrs May to “condemn these ideas” as he noted there had been an “enormous” rise in attacks on Czechs in Britain since the June vote to quit the EU.
“I think the performance at the Conservative Party conference was again stoking the fires.
“When you had all these ideas of British companies that would have to report the number of foreigners they employ, maybe even the names of the foreigners they employ, that is very similar to what we have seen on the continent in the 1930s.
“I think we all remember what it led to. So I think we see it as very dangerous, and I was really hoping that Prime Minister May would condemn these ideas very quickly and it’s not happened. So that is a worry.
“At the moment we need to support the security of Czechs. We’ve seen an enormous increase in attacks on Czechs and other foreigners on British soil,” he told BBC Radio Four’s Analysis programme.
The suggestion by Home Secretary Amber Rudd that companies should count foreign workers was roundly condemned, forcing the Government to state it would not mean that individual non-British staff would be listed.
European Commission president Jean-Claude Juncker also struck a much tougher stance on Mr Trump than London, stating: “I think that we’ll waste time for two years while Mr Trump tours a world that he is completely unaware of.
“We have to teach the new president of the USA what Europe is, and how it works. The trans-Atlantic alliance, and the Nato alliance, is called into question, so it could be quite pernicious.
“With regards to refugees and other non-Americans, Trump has an approach which in no way coincides with the approach in Europe.”
The comments came as Liberal Democrat leader Tim Farron said his party would vote against triggering Article 50, which formally launches withdrawal negotiations with the EU, unless there was a guarantee that the final Brexit deal with Brussels is put to a fresh referendum.
The Government is challenging a High Court ruling that Parliament must have the final say on triggering Article 50 with a hearing in the Supreme Court next month, arguing that prerogative powers could be used to trigger the mechanism.