Around 80 nurseries in the city's East End have given out leaflets for 4,000 children to take home to their parents with basic information on secondhand smoke. Parents who sign up to a 'gold pledge' must agree to a smoke-free home, while those signing up to a 'silver pledge' are limited to smoking in only one room in the house.
Parents opting for the gold pledge are entered into a prize draw for 100 of DIY vouchers.
If the scheme proves successful it is expected to go city-wide.
Brenda McConnell, a tobacco health promotion officer at Greater Glasgow NHS Board, said, 'Up to 17,000 UK children under five get admitted to hospital every year because of the effects of secondhand smoke. A lot of people just aren't aware of the effects.'
There is a concern that Scotland's new ban on smoking in public places will expose young children to more of it at home.
Ms McConnell said that the scheme was not anti-smoking, but about raising awareness that passive smoking can reduce lung growth in children, trigger respiratory problems such as bronchitis or asthma, and cause cot death.
Ms McConnell said, 'The aim is to protect children. The scheme points out that if you are not ready to quit smoking, this is the next best thing you can do.
'We understand that it's difficult to give up. It's not to victimise smokers but to give them practical steps to stop their children being affected.'
Leaflets about the scheme are also distributed by midwives and at doctors'
surgeries. Around 80 families have made a pledge so far. Ms McConnell said, 'One of our parents is a smoker and also a childminder. She took the gold pledge because she felt that it is important for her role as a childminder to set an example.'
Children are one of the most vulnerable groups to passive smoking because they are still developing, breathe faster and have little control over their own environment.