When President Barack Obama travels abroad, sometimes it’s not enough for just the leader of the free world to show up. People in other countries want the first lady, too.

But Michelle Obama won’t join her husband when he heads to Asia this week, and her absence is likely to sting, especially in image-conscious Japan. It’s the first of four countries on Obama’s travel schedule and one of two that are welcoming him with official state visits.

“If Madame Obama could have come, it would have been better. But the most important thing is that President Obama accepted this is a state visit,” said Matake Kamiya, a professor of international relations at the National Defense University in Yokosuka, near Tokyo. “From an expert point of view, it’s sort of worrisome why Madame Obama isn’t coming.”

The fact that Mrs. Obama recently spent a week in China with her mother, Marian Robinson, and daughters Malia and Sasha also is sure to be noted in Japan, a close U.S. ally and China rival. But the first lady’s communications director, Maria Cristina Gonzalez Noguera, said it was not expected that Mrs. Obama would join the president on a return trip to Asia so soon, having returned less than a month ago.

“When it comes to international travel, the first lady has always chosen her trips based on what’s best for her family,” Noguera said in an emailed statement.

The last U.S. first lady who did not join her husband on a state visit to Japan was Gerald Ford’s wife, Betty. Ford became the first sitting American president to visit Japan when he arrived in November 1974, a few months after he took over the office from Richard Nixon.

Anita McBride, who was chief of staff to Laura Bush, said having the president’s wife on his overseas trips is always welcomed — by both the White House and the host country — because she can carry out a different type of diplomacy.

“They can focus on different things and, between the two of them, really spread a lot of goodwill,” said McBride, who heads a first ladies’ project at American University.

When Mrs. Obama does travel with the president, she often gets as much — and occasionally more — local media coverage.

Last year in Northern Ireland, where Obama and other major world leaders gathered for an international summit, she was “the Obama” who got top billing in the local newspaper. The front page of the Belfast Telegraph featured a head-to-toe photograph of Mrs. Obama with the headline, “How Michelle (and a bit of trouble with her fringe) stole the show.” The headline referred to the first lady’s debut of her longer bangs that swept in front of her eyes during a speech to students.

Obama and the summit host, British Prime Minister David Cameron, made the front page, too, but in separate and smaller photos.

Mrs. Obama’s China visit last month was partly seen as making up for her not accompanying the president to California last year for the visit by President Xi Jinping and his wife, Peng Liyuan. The meeting fell days before Sasha’s 12th birthday, and Mrs. Obama’s office said at the time that she stayed back in Washington to be with family.

In public, Beijing muted its hurt feelings over Mrs. Obama’s absence in California. But deep disappointment was registered in some Chinese mainstream and social media.

Many Chinese had looked forward to comparing Peng, an unusually visible and fashionable Chinese first lady, to her glamorous and high-profile American counterpart. Peng holds the rank of major general in the People’s Liberation Army and was a popular singer on state television.

Mrs. Obama made up for her absence in California with a well-received, widely reported visit to three Chinese cities last month. She jumped rope, dabbled in tai-chi, walked a section of the Great Wall with her daughters, fed pandas, met with Xi and ate dinner with Peng.

The Japanese are putting a good face on Obama’s upcoming solo stop, noting that his stay will be short. One high-level Japanese government official chalked up the first lady’s absence to a new “American style” of travel. The official was not authorized to discuss by name details of Obama’s trip before the White House announced them and spoke only on condition of anonymity.

Mrs. Obama’s most recent overseas trip with her husband came last summer, when they visited three African countries with their daughters, shortly after their stops in Northern Ireland and Germany. Since then, the president has traveled without her to Sweden, Russia, Mexico, the Netherlands, Belgium, Italy and Saudi Arabia.