But the first lady told David Letterman on Monday the woman only wanted help with a package she couldn't reach.
During Obama's visit to CBS' "Late Show," Letterman held up a picture of her after she put on sunglasses and a baseball cap to try to visit a Washington-area store last September.
Obama said the woman apparently was oblivious of the fact she had asked a favor of the first lady and said "you didn't have to make it look so easy" after the detergent was retrieved.
"That was my interaction," Obama said. "It felt so good."
The first lady talked about how she learned from her parents the notion of unconditional love, that the most important thing for children to know is that their parents adore them. She said she and the president try to instill that stability in their own two daughters, and almost became emotional talking about her father.
"Don't make me cry," she said. "This isn't `Oprah.' It's supposed to be `Letterman."'
The "Late Show with David Letterman" airs weeknights at 11:35 Eastern time.