The explanation came after Southwest Airlines flight attendant Beverly McCurley reported taking the child from the mother during Monday's flight after seeing the child slapped on the face and hearing passengers complain.
The incident has sparked an online debate about when onlookers should intervene in child discipline.
McCurley also told authorities the child had a black eye.
Both parents told aviation police the black eye came from a dog bite a few days earlier. The mother said an uncle, who had medical training in the military, treated the injury.
Aviation police officer Dana Baldwin said in a written report the mother demonstrated the amount of force she used by lightly hitting the officer's arm with an open hand. The officers did not ask where she slapped the child.
The baby was checked out by paramedics at Albuquerque airport, a scheduled stop on the flight to Seattle.
The names of the parents were withheld because they were not arrested or charged. The family boarded another flight to continue the trip.
Brad Hawkins, a spokesman for Southwest Airlines, could not provide details about specific training given to flight attendants to deal with such situations. However, he said they were "empowered to simply do the right thing and to maintain the security and the comfort of all of customers onboard."
Aviation police met the flight at the gate in Albuquerque at the request of Southwest Airlines and interviewed the parents, the flight attendant and a witness involving the report of parents aggressively disciplining their child.
Baldwin said the mother told him she "popped her when she kicked me and that was it." She told the officer she hadn't done anything wrong.
The mother also told Baldwin the baby was tired and crying, and "when she's screaming and she can't hear me say no, that's the only way I can get her to stop."
Aviation police officer Ernesto Rojas said in the report the mother demonstrated putting her finger on the child's lips to try to quiet her.
McCurley told the officers she saw the mother hit the child on the face with her open hand while the father yelled at the mother to stop screaming at the girl.
CBS News reports officers praised the flight attendant for taking action. "I think," says Albuquerque Police Chief Marshall Katz, "it was a solid move on the part of the flight attendant to take custody of the child. It neutralized the situation. It calmed everybody down."
McCurley described the mother as agitated with the child, said the woman also slapped the baby on the legs and told the child to shut up.
McCurley said she took the baby and walked to the rear of the plane. She said the father came back, took the child and stood there with her until she fell asleep.
The father told the attendant the parents had several arguments about the mother hitting the child, according to the report.
He told police the mother would occasionally "pop" the child to stop her kicking and screaming, but that the baby had never been hit in the face.