The tourism ministry in Cairo said 19 Egyptian pilgrims and a child were killed and 15 were injured in the accident.
"Nineteen people were killed when the bus carrying them turned over on the Hijra road" between the coastal city of Jeddah and the holy city of Medina, Saudi Red Crescent spokesman Khaled Ben Messaed al-Sihli said.
"All the bus passengers have the same nationality of an Arab country except the driver who is Asian," he said.
Another 22 people were injured including some who were badly hurt, Sihli added.
Millions of Muslims visit Saudi Arabia each year for the year-round umra minor pilgrimage and the annual hajj pilgrimage.
Jordan said on Wednesday that 14 pilgrims died and another 36 were injured in another bus accident in southern Jordan near the Saudi border.
The country's civil protection service said the driver lost control of the vehicle which turned over 320 kilometres (about 200 miles) southeast of Amman.
A stampede during the hajj last September killed about 2,300 foreign pilgrims, according to data from foreign officials.