The president, who had already insulted the Mayor of London before he even landed on British soil, appeared to grasp only the monarch’s fingers in his fist as he was welcomed to the Palace.
Photos of the unorthodox clinch quickly provoked bafflement and mockery on social media, where many likened it to a fist bump or a complicated multi-part “ghetto” handshake.
Mr Trump and wife Melania were also met as they disembarked from his helicopter on the Buckingham Palace lawn by Prince Charles and the Duchess of Cornwall, who received much more conventional greetings.
The first couple were also due to join the royals for a private lunch followed by a tour of Westminster Abbey.
Not joining the party is the Duchess of Sussex, who is still recuperating after giving birth last month.
American-born Meghan called Mr Trump “misogynistic” and “divisive” during the 2016 election campaign. In an interview with The Sun ahead of this week’s visit the president hit back, saying he was surprised that the Duchess would be so “nasty”.
According to the Royal Family’s website, there are no “obligatory codes of behaviour” when meeting the Queen.
However, if someone does wish to follow the “traditional” etiquette, the website recommends men bow their heads or “shake hands in the usual way”.
Today’s handshake farrago is not the first time the way Mr Trump greets other world leaders has been under the spotlight.
The pugnacious tycoon is famed for his aggressive handshakes and has previously been known to grab the other person’s hand and yank them towards him in an apparent show of dominance.
In 2017, Mr Trump shared an awkward 30-second long clinch with the French president Emmanuel Macron, with neither leader seemingly willing to be the one to first release the grip.