Dr Muhannad Al Zabn, who has a Jordanian father and a Saudi mother, delivered the baby one month ago at the King Fahad Medical City in the Saudi capital Riyadh.
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.
He added that the security authorities launched an investigation after collecting evidence from the scene of the attempted murder.
Most social media users shared their sympathy with the obstetrician and harshly criticised the shooter.
However, some commenters argued that women gynecologists should always be given priority in the delivery of babies in order to avoid cultural clashes.