The video, which was posted on YouTube, showed one of the women holding the baby's neck and forehead while squeezing its face.
Her two colleagues watched and laughed.
The baby had been admitted to the children's hospital in the Saudi city of Taif with a urinary tract infection.
Abdulhadi Al-Rabie, Taif Health Affairs spokesman, confirmed the women had been fired for mistreating the baby.
The baby's father told reporters that he had been shocked by the video, which racked up 57,000 views in two days.
He called on the Ministry of Health to take tough action on the nurses and those who had circulated the video, according to a report in the Saudi Gazette.
The nurses have not been publicly identified but have had their licences revoked.
Al-Rabie said the nurses would face severe penalties if investigations found them guilty of abuse.