The official SPA state news agency quoted Colonel Abdullah al-Harethi as saying people died in several areas including in the capital Riyadh, Baha in the south, Hail in the north and in the west.
Harethi urged people to avoid wadi valleys and plains that have been flooded by heavy rainfall that began on Friday.
Television footage showed 4X4 cars stuck in the middle of wadis and people clinging to a tree to escape fast-flowing flood waters.
The vast Arabian Peninsula country has not experienced such a high volume of rainfall for 25 years.
But around 10 people were killed in 2011 when flooding swept through the western city of Jeddah, where 123 people also perished in floods in 2009.
The inability of Jeddah’s infrastructure to drain off flood waters and uncontrolled construction in and around the city were blamed at the time for the high number of victims.