The man, who has not been named, is believed to have wanted a female doctor to deliver the baby and was upset that the male doctor would have seen his wife naked.
According to media reports, the father went to the hospital and told the doctor he wanted to see him to thank him for helping his wife with the delivery of the baby, Saudi news site Sabq reported on Thursday.
The two met in the garden of the hospital and during the conversation, the shooter took out a gun he had concealed under his clothes and fired at the doctor.
As the Saudi father fled the scene, medics rushed the victim to the emergency department then to the intensive care unit. The shooter was later arrested by the police. Bassam Al Buraikan, the spokesperson for the hospital confirmed the incident, saying that a doctor was shot and that his condition was now stable.