"I didn't know what to do," Jolene Jackinsky, who noticed a man resembling the ex-president in the Signature Flight Support waiting room, told Alaska Dispatch News.
After Obama approached and inquired about Jackinsky's infant, he ended up with the 6-month-old in his arms and smiling for the camera.
"He talked about how fast kids grow up," she said. "He said his daughter is going into college pretty soon. He asked if I had a phone to take pictures and did a selfie with us."
Images of the ex-president, along with mom and daughter, spread across social media, with viewers expressing their delight at the infant's wide-eyed expressions.
Jackinsky told reporters that as her husband approached, Obama joked: "Hey! I'm taking your baby."
The former president was reportedly on his home from a trip to Indonesia. He was accompanied by two Secret Service agents.
Jackinsky was on her way to the place where she grew up, Newhalen, to put up subsistence salmon.