The ban targets most public places such as restaurants, cafes, schools, universities, hospitals, parks, movie theaters, museums and public transport.
The law, which also forbids the sale of cigarettes to minors, was approved six months ago by President Bashar Assad, a British-trained eye doctor.
The Middle East's favorite pastime — smoking water pipes — is also prohibited in public under the new law except in well-ventilated and designated areas. Also outlawed are tobacco advertising and the sale and import of sweets and toys modeled after tobacco products.
Offenders will face fines ranging between $45 and $870 and a possible three to 12 months in jail.
"The ban is good, but I doubt I will stop smoking," said businessman Bassam Shanna, 47.
The ban's effects are already being felt in Damascus' famous cafes.
The normally bustling indoor area of the Nowfara Cafe in the city's downtown area was almost entirely empty on Wednesday.
"Fifty people would be sitting here if it weren't for the ban" complained the manager, Shadi Rabbat.
However, the cafe's terrace was crowded with some 50 customers smoking water pipes.
"We hope the government will reconsider the ban," said another cafe owner who refused to give his name because he feared reprisals by the authorities.
Syria had in the past taken steps to try to restrict smoking, including a 1996 decree issued by Assad's late father, President Hafez Assad, that banned smoking in government offices, hospitals and the airport.
A 2004 law banned smoking in internet cafes and another law in 2006 made buses, railway stations, movie theaters, parks and cultural centers smoke-free, with violators facing a fine of about $10 and three months in jail. But the bans were often flouted and not strictly enforced.
This time, however, more sweeping measures were being taken, reflecting Syria's desire to join other Arab countries struggling to control smoking with bans and anti-smoking campaigns.
Fines are also steeper this time round — the fine for smoking in a cafe is $45 while it goes up to a staggering $870 in five-star hotels.
Health ministry officials will be frequently carrying out on site inspections to ensure the law was being observed in public places.
"It's a chance for me to seriously try to quit smoking," said Mohammed al-Kash, a sociology professor at Damascus University. "I am fully committed to the ban."
Three million people — or 15 percent of Syria's 23.5 million population — smoke. As much as 23 percent of these are university students, according to figures published in the state media. Syrians are thought to spend $565 million a year on smoking.
Other Arab countries are also struggling to create a more smoke free environment.
In the tobacco-loving Arab world, people smoke in offices, universities, taxis, hair salons and even hospitals and smoking has long been a social imperative and a rite of passage for young men.
Packs can cost as little as 50 cents in some Arab nations.
The Palestinian Authority in the West Bank, for example, has no laws banning smoking in government offices or public places, and government employees — including President Mahmoud Abbas and Prime Minister Salam Fayyad — regularly smoke in their offices.
Associated Press writers Hadeel Al-Shalchi in Cairo, Ben Hubbard in Ramallah and Scheherezade Faramarzi in Beirut contributed to this report.