"The first evacuation vessel from Sudan has arrived, carrying 50 (Saudi) citizens and a number of nationals from friendly countries," the state-run Al-Ekhbariya television said.
It aired footage of large vessels arriving in Jeddah's port, and also released a video showing women and children carrying Saudi flags on board one of the ships.
Those who have arrived in Jeddah include the crew of a Saudi passenger plane that was hit by gunfire while preparing to take off from Khartoum at the start of the fighting on April 15, according to Saudi state TV.
A convoy of vehicles carried the evacuees to Port Sudan from where they boarded ships to Jeddah, according to the Saudi broadcaster.
Hundreds have died due to the battles between forces loyal to army chief Abdel Fattah al-Burhan and his deputy turned rival Mohamed Hamdan Dagalo, who commands the powerful paramilitary Rapid Support Forces (RSF).
Heavy gunfire, loud explosions, and fighter jets roared in many parts of the capital Saturday morning, according to witnesses.