Obama is seen sending up "birther" theorists who demanded to see his long-form birth certificate in the video, as he claims that White cannot really be 90 years of age.
Penning a card for the Hot in Cleveland star in the Oval Office, the president says in voiceover: "Dear Betty. You look so fantastic and full of energy, I can't believe you're 90 years old. In fact, I don't believe it. That's why I'm writing to ask if you will be willing to produce a copy of your long-form birth certificate."
"Thanks, and happy birthday - no matter how old you are."
Obama is then seen placing a framed photograph of White alongside pictures of his family and listening to the Golden Girls theme tune through headphones at his desk, nodding in time.
The clip aired as part of NBC special Betty White's 90th Birthday: A Tribute to America's Golden Girl. The show attracted 13.85m viewers to the network on Monday evening (January 16), while her new series Betty White's Off Their Rockers pulled in 12.23m.
Obama's wife Michelle shares her birthday with White - the first lady turned 48 on Tuesday (January 17).
> Betty White gets standing ovation at People's Choice Awards 2012
Watch a clip of Betty White performing the 'anthropology rap' during the second season premiere of Community below: