The law, approved last May, was one of the sparks for anti-government protests that swept the country last June and was used by activists as an example of Prime Minister Recep Tayyip Erdogan's attempted "Islamisation" of the largely secular country.
The new law forbids the sale of alcohol between 10pm and 6 am (local time) in shops, as well as at any time near schools and mosques.
Bottles will have to display messages warning of the dangers of drinking, and advertising of alcoholic beverages will be banned on university campuses and television.
Erdogan, a pious Muslim who neither smokes nor drinks, has defended the law on health grounds. But Turkey's sizeable secular population has denounced the law as repressive and with religious, not social, motivations.
The prime minister has previously provoked outcry when he suggested that Turkey's national drink should be ayran, a yoghurt and water-based concoction, rather than reki, the country's famously strong aniseed-flavoured spirit.