The former President wished the former First Lady a HBD by sharing a series of adorable black-and-white photobooth pics. He captioned it ... "In every scene, you are my star" and added an emphatic, "Happy birthday, baby!"

Barack showed his wisdom by not revealing her age, but for the record ... Michelle's celebrating #56 today.

Her birthday caps off a great week for the Obamas -- a documentary film they produced, "American Factory," landed them an Oscar nomination Monday.

The couple also spent a lot of the recent holiday season having fun in Hawaii, and Barack was named the most admired man in 2019. Of course, he tied with President Trump for that honor ... so ya can't have it all.