There is video circulating of what appears to be the 19-year-old blowing smoke rings in a bathroom.
The president's daughter tweeted, "Malia Obama should be allowed the same privacy as her school aged peers. She is a young adult and private citizen, and should be OFF limits."
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Chelsea Clinton also came to the defense of Malia tweeting, "Malia Obama's private life, as a young woman, a college student, a private citizen, should not be your clickbait. Be better."
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The former first daughter is a first-year student at Harvard University. Malia took a gap year after graduating high school in 2016, in what the Obamas said was an effort to start college without the distraction of her father in the White House.
The informal society of presidential children has historically been protective of its youngest members, without regard for political party.
The Associated Press contributed to this report.
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