Obama arrived in Japan on Wednesday for the first part of his Asia trip that includes visits to South Korea, Malaysia and the Philippines.
Keith Koffler, a veteran White House correspondent, noted on his White House Dossier blog that the first lady could not join Obama as she had to attend a Democratic National Committee fundraising event.
The White House did not respond to a request for comment.
This is not the first time Obama has been accused of cheating on his wife.
American newspaper National Enquirer reported in January that the couple is sleeping in separate bedrooms and the president will allegedly return to Hawaii when his term ends, while his wife and their daughters will stay in Washington.