The blaze broke out at the intensive care unit and the maternity department of the Jazan general hospital in southern Saudi Arabia, the civil defence agency said on Twitter.
The agency said later that the fire had been extinguished and an investigation was under way into the cause.
Twenty-one civil defence teams had assisted in putting out the blaze, it added.
Daily newspaper Alriyadh quoted a civil defence spokesman as saying the agency was alerted to the fire at 2am.
In August, 10 people were killed and 259 wounded in a fire at a residential complex rented by oil giant Saudi Aramco in the kingdom’s Eastern Province. That fire was ignited by an electric short circuit in the in the underground car park, according to the authorities.
Thursday’s fire sparked a wave of criticism from social media users who complained that Jazan province, especially its hospitals, suffered from inadequate infrastructure.
A Twitter user named Ahmed said the province “had been neglected by the state” for decades.
“Maybe this catastrophe could put the spotlight on the disastrous situation of hospitals in Jazan … Even though we have little hope,” wrote another user.
Others called for the health minister, Khalid al-Falih, to be sacked.
Civilians in Jazan have also been victims of frequent missile attacks by Iran-backed rebels in neighbouring Yemen, where a Saudi-led coalition has been battling the Shia Houthi insurgents and their allies since March.