The ban includes smoking of water-pipes, or shishas, and prohibits selling tobacco to those under the age of 18.
The official SPA news agency says Interior Minister Prince Ahmed bin Abdulaziz has ordered that a royal ban on smoking be implemented as of Monday. He is cited as saying that Islam urges the preservation of public health.
The ban is a significant step-up in the kingdom's anti-smoking campaign. Saudi Arabia banned smoking in its airports last year.
Saudi statistics say the country is the world's fourth largest importer of tobacco and that six million Saudis spend about 30 million Saudi riyals (about $8 million) a day on cigarettes.