Outside those exceptional areas, curfews will be eased between 9 a.m. and 5 p.m. (0600-1400 GMT) effective Sunday until May 13. The Muslim fasting month of Ramadan began on Friday.
The royal order also allowed some economic and commercial activities to re-start, including wholesale and retail shops and shopping malls, from Wednesday until May 13.
Activities which do not allow for physical distancing, including salons and cinemas, will remain closed. Social gatherings of more than five people are forbidden.
Authorities in the capital Riyadh issued additional advice saying banknotes were not to be used.
Shops that do open should ensure no more than one customer per 10 square metres. Malls must be sterilised every 24 hours and children under 15 are not allowed to enter.
Saudi Arabia has recorded 16,299 cases of infection with the new coronavirus and 136 deaths. These are the highest numbers in the six-member Gulf Cooperation Council (GCC), which together have recorded almost 43,000 cases and 250 deaths.