Second-hand smoke is estimated to cause more than 20,000 cases of respiratory infection in children and account for one in five cot deaths in the UK each year, according to the Scottish Government.
Public health minister Michael Matheson said every child should have the chance to grow up in a smoke-free environment.
"This campaign isn't about a person's choice to smoke, it's about people who smoke having the facts so they can smoke in a way that doesn't harm their children," he said.
"The reality is that many think they're already doing enough, without realising that the harmful chemicals from second-hand smoke linger, even when there is no smell and it can't be seen. Because children's immune systems aren't fully developed and they breathe quicker than adults, the simple fact is that smoking in the home or car puts children of all ages at risk.
"We are absolutely clear on our commitment to prevent people taking up smoking and helping those who do smoke to quit. We have led the way with the ban on smoking in public places, the display ban and our commitment to a tobacco-free generation.
"But where people do smoke, it is crucial they know the full facts about the harmful impact it has not just on them, but those around them such as their children."
The campaign sets a target to "spare" 50,000 children from exposure to second-hand smoke. It means reducing the proportion of exposed children from 12% to 6% by 2020. Scotland is now the first country in the UK to set such a target.
The campaign aims to give smokers information to help them understand how smoking indoors pollutes the air.
Dr Sean Semple, of the University of Aberdeen, helped to inform the campaign.
He said: "In the past five years our research group has measured pollution levels in over 100 homes across Scotland. Smoking homes have very high concentrations of fine particles that tend to be much higher than the worst pollution on even the busiest roads in Scotland.
"Second-hand smoke also lingers for a long time. In more than a fifth of cases it took over five hours for the second-hand smoke to clear and during this time the harmful chemicals will move around the house.
"Despite the high second-hand smoke levels measured, the outlook is good. Many of the smokers we worked with were already starting to make their home smoke-free. By taking their smoking right outside people can improve the air quality in their home and protect the health of their families."
James Cant, head of British Lung Foundation Scotland, said: "Everyone knows that cigarette smoke is harmful. What we don't all know is that more than 85% of smoke is invisible and has no smell. That hidden danger can linger and kids who are exposed are at greater risk of diseases from glue ear to asthma, meningitis and cot death."