In his 2013 bracket, he has Baylor defeating Notre Dame in the April 9 final in New Orleans, a repeat of last year's NCAA title matchup.
The president also selected Connecticut and California to advance to the Final Four. Baylor features 6-foot-8 dunking sensation Griner, who Obama said has "just been spectacular."
Griner's team is on a 30-game winning streak after an early loss to Stanford.
Obama's picks were announced Friday on ESPN. He filled out his bracket Tuesday before departing on his Middle East trip. He chose Indiana to beat Louisville for the men's title.
Obama also praised Skylar Diggins, saying the Irish guard competes with "a lot of poise, a lot of heart."
He has sixth-seeded Delaware — Vice-President Joe Biden's home state — and standout Elena Delle defeating West Virginia and North Carolina in the early rounds. Obama said his daughter Sasha plays in a recreational basketball league with Biden's granddaughter.
"Women players have gotten so much better than they were even 10 years ago," he said. "The athleticism, the skill levels. You're seeing how it's impacting younger kids."
Baylor, Connecticut and Notre Dame are the No. 1 seeds and California is a No. 2 seed. The women's tournament starts Saturday.