When the plane landed in Albuquerque, the family was met by police. A Southwest Airlines spokeswoman told ABC News the local authorities were called "out of precaution for the child."
The parents were questioned by police and released to continue to their final destination.
According to a report from Albuquerque police, the parents, Lee Ann and Joseph Cid, were arguing on the flight, trying to get their 13-month-old daughter to stop crying, when the flight attendant, Beverly McCurley, intervened.
"She informed me several passengers had reported that a female subject traveling with a baby and her husband had been observed striking the child on the face in an attempt to get the child to stop crying," wrote the reporting officer.
"McCurley further stated she walked to the rear of the aircraft and observed the mother of the child identified as Lee Ann Cid strike the child with an open hand on the face in an attempt to get the child to stop crying. McCurley further stated the mother appeared agitated with the child and that the husband continued to yell at his wife to shut up due to her screaming at the child."
According to the police report, McCurley said the child had a black eye, but the parents blamed that on an uncle's dog.
"McCurley then stated she took the child from the mother due to her behavior and walked to the rear of the aircraft with the child identified as a 13-month-old female," said the police report. "McCurley then stated the father identified as Joseph C. Cid walked back to the rear of the aircraft, took custody of the child and stood on the rear of the aircraft until the child fell asleep."
Police said McCurley did the right thing, and said the parents were not abusing their daughter.
"I think it was a solid move from the part of the flight attendant to take custody of the child," said airport police chief Marshall Katz. "It neutralized the situation, it calmed everybody down."
Southwest Airlines representative Whitney Eichinger confirmed to ABC News that there was an issue on the flight, but denied accounts that the flight attendant took the young child from its parents.
"What you read about the flight attendant taking the baby is not the case. She did it as a 'Would you like me to bounce your baby for you?'" Eichinger said.
"The family on board was having an altercation and their young child was upset. Our flight attendant offered to the parent -- offered to hold the child on board. Our attendants do that from time to time just to soothe the crying babies because they are used to walking up and down the aisles."
When called for clarification, the Albuquerque Sunport Police maintained that the child was taken into custody by the flight attendant.
The incident took place on board Monday's Southwest Flight 879, which originated in Dallas and stopped in Albuquerque before continuing to Seattle.