Saudi Arabia's Al Watan newspaper reported that two people were killedand that the flooding caused 275 car accidents.
Prince Faisal bin Abdullah, Saudi Arabia's minister of education, announced that schools would be closed in Riyadh on Tuesday, with colleges and universities following suit.
Authorities also announced a state of emergency, and told residents not to use their vehicles unless necessary.
Flights at Riyadh's King Khaled International Airport were unaffected by the rains, although airport officials say nearly half of the afternoon's scheduled passengers missed their flights because of the poor road conditions.
Residents of Riyadh posted dramatic picturesand videoof the flooding online, including on YouTube and a number of blogs.
Online activists also launched the website RiyadhRain.comto help locals monitor the developing situation, while Twitter users organised aid and warned others of the city's worst-affects areas with the #riyadhrainsearch tag.
Authorities saids dozens of teams of municipal employees had been assigned to pump water from Riyadh's flooded streets after Monday's downpour.
The Saudi government was sharply criticised last November for its poor response to flooding in Jeddah.
More than 120 people were officially killed, although hundreds were reported missing after some of the worst rains to hit Saudi Arabia a decade. Some roads accumulated more than one metre of water, and many of the victims were drivers who drowned in their cars.
Jeddah businesses estimated their damages at more than $270 million.
Flash floods also killed seven people in southwestern Saudi Arabia last month.