SPA, citing a source with the Interior Ministry, said entry and exit will be prohibited from the province.
Authorities also brought forward a curfew in the province to start at 3 pm local time (12:00 GMT) instead of 7 pm (16:00 GMT).
Last week, Saudi authorities imposed a three-week curfew and locked down Riyadh and the holy cities of Makkah and Madinah to curb the disease.
Saudi Arabia has reported three deaths from the virus and over 1,100 confirmed cases.
Data compiled by the US-based Johns Hopkins University shows worldwide infections over 666,200 mark with over 30,800 deaths. More than 141,700 have recovered from infections.
After first appearing in Wuhan, China in December, the virus has spread to 177 countries and regions.