The storm, which struck during Tuesday evening's rush hour, had subsided by daybreak Wednesday but some roads were still inundated.
Riyadh implemented its emergency plan to deal with the flooding, the spokesman for the municipal council, Mohammed al-Shwayman, was quoted by the official Saudi Press Agency (SPA) as saying.
Residents were urged not to gather in affected areas "for the sake of taking pictures and videos, putting their lives at risk," he said.
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Traffic backed up for kilometres (miles) along at least one major thoroughfare and many vehicles broke down as the deluge flooded city streets.
Riyadh, an inland desert city of 5.7 million, is famed for its searing temperatures and sees only occasional bursts of rain.
The Arab News daily cited the education department as saying all schools in the capital region would be shut on Wednesday.
SPA reported that at least one university, the Naif Arab University for Security Sciences, had also suspended classes.
In the kingdom's southwest, classes were suspended in the Asir region "due to weather conditions," an official cited by SPA said.