The 18-year-old, who is set to attend Harvard next year, was at the Lollapalooza music festival in Chicago, Illinois, where a nine-second video published by Radar Online, apparently captured her smoking, is doing the rounds on internet and has evoked mixed reactions from public.
The website claimed an eyewitness smelled cannabis in the air, the Telegraph reported.
Cannabis is decriminalised in the state of Illinois and people are allowed to possess up to 10 grams of the drug.
The first daughter missed Hillary Clinton's speech at the Democratic National Convention last month to go to Lollapalooza.
Previous video had emerged of her "twerking" at the festival.
Her father had previously admitted smoking cannabis as a youth and he was part of a group of friends known as the "choom gang" in Hawaii.
Malia is currently on a gap year before going to Harvard in the autumn of 2017.
At the Democratic Convention, her mother Michelle Obama spoke movingly about her effort to give Malia and younger sister Sasha a normal life.
Sasha Obama, 15, has undertaken a summer job in a fish restaurant in Martha's Vineyard.
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Video courtesy: Mango News/YouTube