The television station, WPBF in West Palm Beach, said the 18-month-old's parents asked not to identified because they were worried about being profiled during future airport security searches.
They told the station that they believed their daughter was singled by TSA officials because of their appearance.
"It's absurd," the child's father said to the TV station. "It made no sense. Why would an 18-month-old child be on a no-fly list?
"We were put on display like a circus act because my wife wears a hijab," he continued.
On its website, TSA says of its "Secure Flight" program "[I]f a passenger successfully obtains a boarding pass, his/her name is not on the No Fly List.
"If a passenger feels they have been misidentified, redress is an opportunity to seek resolution and avoid future delays," the TSA website says. "Any passenger who believes he/she has been delayed or denied boarding or delayed or denied entry into the United States at a port of entry may seek redress through the Department of Homeland Security (DHS) Traveler Redress Inquiry Program (TRIP) at www.dhs.gov/trip."