I couldn't find the actual law itself, but this came from the Gulf Times;

Smoking is already prohibited in most public places in the country, according to Law No 20 of 2002, on the control of tobacco and its derivatives.

[..]

The ban covers public transport, schools, educational and training centres, universities, health centres, ministries and government departments, inside lifts, cinemas, theatres, shopping centres, sports clubs, industrial establishments and restaurants and shops selling food and beverages.

In the same article an official also said that members of the public need to be vigilant and start reporting offenders.