Anyone caught smoking in a vehicle in front of a child or youth under the age of 18 will be fined 100 euros (£73).
Failure to pay the fine, or to stop a vehicle and give personal details to the police could lead to a prosecution and 1,000 euros (£727) penalty.
A similar ban is being considered by the Northern Ireland Assembly.
Earlier this month, Stormont Health Minister Simon Hamilton announced an amendment to a bill currently going through the assembly, which if passed, would now mean smoking in cars with children would be illegal anywhere on the island of Ireland.
The Irish government signed its ban into law this week, under the Protection of Children's Health (Tobacco Smoke in Mechanically Propelled Vehicles) Act.
The details were announced by Minister for Children Dr James Reilly and Minister for Health Leo Varadkar.
Mr Reilly said it was a central part of his government's "Tobacco Free Ireland" policy.
"The Irish Health Behaviour in School-aged Children (HBSC) Study 2014 found that nearly one in every five children between the ages of 10 and 17 years are exposed to toxic, carcinogenic smoke in cars," he said.
"Even if windows of the car are open the young person is not protected from the harmful effect of second-hand smoke."
Mr Varadkar said: "Children are more susceptible to the effects of second-hand smoke and may not be able to avoid exposure.
"Second hand smoke is particularly harmful to children in enclosed spaces, such as cars."
Under the new law, drivers and passengers will be banned from smoking cigarettes, cigars or pipes when they are inside a vehicle with someone under the age of 18.
Drivers will also be held responsible if they allow their passengers to smoke in front of children.
The legislation does not apply to electronic cigarettes, which are exempt from the ban.
In Great Britain, a law banning smoking in vehicles carrying children came into force in England and Wales in October.
The Scotland government is planning to legislate on the issue next year.

Profits for the July to September period are forecast to be 5.6% higher at 7.8 trillion won ($7bn; £5.7bn).
Analysts had expected worse numbers after the Note 7 recall over faulty batteries and "exploding" phones.
The earnings guidance does not give any details about the performance of individual businesses.
The flagship Galaxy Note 7 was recalled in 10 markets around the world, including the US, Europe and South Korea.
Some estimates had suggested the recall would reduce Samsung's profits by 1tn won or more.
However, a strong performance by its chip and display business is expected to have offset some of those losses.
The earnings guidance did not comment on calls by investors to radically restructure the firm into two separate holding and operating companies.
On Thursday, Samsung had said it was "carefully reviewing" the suggestion.
A ban on smoking in vehicles when children are present will come into effect in the Republic of Ireland on New Year's Day, 1 January 2016.
[NEXT_CONCEPT]
Samsung Electronics says its operating profits are expected to have risen in the third quarter, despite the recall of its Galaxy Note 7 smartphone.