Angus Brochan, MP for Braeburn East, quipped "Been through so much...champagne".
The Tweet is believed to refer to a scar on Princess Eugenie's back from an operation for scoliosis aged 12, which was visible above the dipped back of her wedding gown. The condition causes the spine to misalign and make the back appear hunched.
Earlier this year she revealed for the first time her own x-rays showing the damage to her spine and ahead of the wedding spoke of the importance of "showing people your scars".
However President Trump's effusive message was in stark contrast to his silence on Twitter following the marriage of Prince Harry to Meghan Markle, after he was snubbed from the wedding.
During the US election campaign in 2016, Miss Markle, now the Duchess of Sussex, told The Nightly Show with Larry Wilmore than she believed Mr Trump was misogynistic and divisive.
President Trump and wife Melania did make a charity donation as a wedding gift to the Duke and Duchess, but made no public declaration of congratulations.
The Duke and Duchess did not meet the President and First Lady during an official visit in July.