The video was posted to social media Thursday and involved a worker and a child at My Little Playhouse Learning Center in Lubbock, the television station reported.
Police investigators, who are referring the case to prosecutors on possible assault charges, said the video was recorded Dec. 26. However, the child's parents were unaware of the recording until it hit social media, KCBD reported.
The video shows an employee at the day care center grabbing a young child by the hair as the girl tried to stand up, the television station reported.
The person recording the video can be heard laughing and making fun of another child, KCBD reported.
"They had no apology," the child's mother told KTRK. "They had no reason they did not call me. Like I said, everything hit the fan and it's like they just had nothing to say."
The two employees involved in the incident were fired, day care officials told the television station.