The vehicle overturned on the road between Mecca and Medina, Mena said.
There were 44 Egyptian pilgrims on board the bus when it crashed, the agency said.
The incident comes just days after 16 Palestinian pilgrims from the West Bank were killed when their bus crashed in Jordan on its way to Saudi Arabia.
The groups were both travelling to Mecca to perform the lesser Islamic pilgrimage, or Umrah.
Nineteen people have been killed after a bus carrying Egyptian pilgrims crashed in Saudi Arabia, Egypt's state-run Mena news agency says.