Several local municipalities tweeted the directives, which Saudi-owned Al Arabiya television said would apply across the country.
Saudi Arabia has also temporarily suspended government work and ordered public-sector workers to stay home for 16 days.
Only those working in health, security and the military are exempted from the decision to stop people attending the workplace.
The measures come as the kingdom announced 15 new cases on Sunday, taking the overall number to 118.
Saudi Arabia has also halted international passenger flights, canceled Umrah pilgrimages and locked down the eastern Qatif region.