Destenay, a Belgian architect, married Bettel in 2015, becoming the first same-sex spouse of a leader of a European Union member state, the Guardian reported on Saturday.
American First Lady Melania Trump was identified twice in the original caption to the official White House photograph, which was taken by Andrea Hanks and posted to Facebook on Saturday in a collection of pictures from Trump's nine-day international tour.
Destenay's name later appeared in an edited version of the caption.
The original caption read: "First Lady Melania Trump poses with Belgium's Queen Mathilde, center, and other spouses of Nato leaders: First Lady Emine Erdogan of Turkey; Iceland's Thora Margret Baldvinsdottir; the First Lady of France Brigitte Trogneux; First Lady Melania Trump; Slovenia's Mojca Stropnik; Bulgaria's Desislava Radeva; Belgium's Amélie Derbaudrenghien, and Norway's Ingrid Schulerud."
Destenay, smiling and wearing a dark suit, white shirt and light blue tie, is clearly visible in the picture, behind Melania Trump's right shoulder, reports the Guardian.
The "mistake" faced a lot of criticism and backlash on social media.
Scott Bixby of the Daily Beast called the caption "homophobic".
Destenay and Bettel's marriage is not the first same-sex union at the highest levels of world politics.
In 2010, Johanna Siguroardottir, then Prime Minister of Iceland, became the first serving leader in the world to marry a same-sex partner.