The Council of Senior Scholars said Muslims should "avoid gatherings, because they are the main cause of the spread of infection", the state-run Saudi Press Agency reports.
Sunni-majority Saudi Arabia has closed its mosques, including the world's holiest - the Grand Mosque in Mecca - as part of measures to try to stop people catching the virus.
Meanwhile the Supreme Leader of Shia-ruled Iran, Ayatollah Khamenei, has said Muslims are not required to fast during Ramadan - one of its obligations - if doing so poses a threat to their health.
(BBC News)