Campaigners from smokers' group Forest have criticised the ban as an example of "creeping prohibition".
Cities including New York, Toronto and Hong Kong have already banned smoking in key outdoor locations but Bristol is the UK's first to pilot smoke free zones.
Millennium and Anchor Squares are home to the At-Bristol science museum, shops and restaurants, and are well-used play spaces for children.
Two squares in Bristol will become the first major public outdoor spaces in UK to go smoke-free.
From today a voluntary smoking ban will be in place in Millennium Square and Anchor Square. The area is home to the At-Bristol science museum and often hosts festivals and other family friendly events.
The project is part of the Smokefree South West campaign.
It's been announced that a whole month dedicated getting people to give up smoking will return for another year.
Last year October became Stoptober and 160,000 people quit smoking nationally as a result.
The health bodies behind it, including Smokefree South West, say that, if people can stop smoking for 28 days, they are five times more likely to stay smokefree.
They also say it will add up to seven days to their lives.
Two sisters from Bath, Sylvia and Pat, are warning against smoking after seeing the damage it caused to each other.
It comes as a new hard-hitting advertising campaign aimed at raising awareness of the fifth biggest killer in Britain has been released today.
Smoke free South West say 90,000 people in the region currently suffer from Chronic Pulmonary disease but another 55,000 might not know they even have it. The charity hopes the advert will change that.
The anti-smoking group, Smokefree South West has begun a hard-hitting advertising campaign to get people to give up. It's being backed by sisters Sylvia Beever and Pat Bayley from Bath.
They were both smokers but Pat quit when her sister fell seriously ill with chronic lung disease. There are 90 thousand people in the region being treated for the condition but it's believed that there are another 55 thousand who are ignoring the symptoms.