Melania Trump, the third wife of the current US President, posted a photograph on her Twitter.
After Donald Trump won the November election, he and Melania announced that she would stay in New York and move to the White House until Barron Trump, 11, finished the academic year at his school.
Barron Trump wore a T-shirt with words "The Expert" written on it.
Barron will be the first boy to live in the White House since 1963 when John F. Kennedy Jr. was 3 years old.
Mainstream media reported that such a long separation between the president and his family was "unprecedented," describing Melania's decision as disregarding "the most basic of all first lady traditions." CNN reported on the cost of the additional security services provided for the president's family in New York, which taxpayers had to cover.