Children are exposed to "unacceptably high levels" of alcohol marketing through sports sponsorship and public adverts, according to a report.
Alcohol Focus Scotland (AFS) said there was "clear evidence" that exposure to alcohol marketing led children to start drinking at a younger age.
It has called for the Scottish government to take action.
The government wants a minimum-unit price for alcohol but the move has been delayed by a legal challenge.
Aileen Campbell, the minister for public health and sport, said: "This is an interesting contribution to the debate on alcohol policy in Scotland and we will consider it carefully.
"We've been clear that more should be done to protect children from unsuitable advertising. However, the regime governing broadcast advertising is reserved to Westminster and as a result we have pressed the UK government on this issue."
AFS is calling for a ban on alcohol adverts in streets, sports grounds and public transport, alcohol sponsorship of sport, music and cultural events, and restrictions on adverts in newspapers and on social media.
It is also pressing the UK government to restrict TV alcohol advertising between 06:00 and 23:00 and cinema advertising to 18-certificate films.
Organisations including Children 1st, the Scottish Cancer Prevention Network and the medical Royal Colleges are supporting the AFS campaign.
The report - which involved experts in alcohol marketing, legislation and public health - also recommended that an independent taskforce outside the industry is set up.
Prof Gerard Hastings, part of the expert group, said: "Self-regulation does not work; it will not control dishonest banks, over-claiming MPs or profit-driven multi-national drinks companies. Yet we continue to rely on it to protect our children from alcohol marketing.
"It is no surprise that study after study has shown that, as a result, children are being put in harm's way - and that parents want policymakers to be more courageous.
"Scotland now has a chance to grasp this nettle and show how independent statutory regulation of marketing can provide our young people the protection they deserve."
AFS chief executive Alison Douglas said: "An alcohol-free childhood is the healthiest and best option, yet we allow alcohol companies to reach our children from a young age.
"They are seeing and hearing positive messages about alcohol when waiting for the school bus, watching the football, at the cinema or using social media.
"We hope ministers will respond to this report and the groundswell of support for effective alcohol marketing restrictions in Scotland."
Scotland's Children and Young People's Commissioner Tam Baillie said: "I strongly support this report which provides clear evidence on the nature and reach of alcohol marketing, and makes welcome and sensible proposals to safeguard our children.
"All children and young people have the right to good health and that must include the right to grow up free from commercial pressures to drink alcohol.
"The extent of the actions we take now are a good measure of the value we place on our children for the future."
'Catalyst for action'
Julie Hesketh-Laird, acting chief executive of the Scotch Whisky Association, said: "The Scotch whisky industry is rightly proud of its long-running and significant financial support of a diverse range of community and national sporting and cultural events, from local Highland games, to literary awards and live music.
"Many events, and related jobs across the country, would not exist without industry sponsorship and the subsequent benefits to our economy and society, as well as Scottish tourism, would be lost.
"Through a combination of existing regulation and a robust industry-wide code of practice, there is already a strong framework in place to ensure the responsible marketing and advertising of our national drink, with the industry taking its responsibilities seriously."
Scottish Labour's inequalities spokeswoman Monica Lennon welcomed the report.
She said: "Reducing children's exposure to unhealthy alcohol marketing is pivotal to improving public health.
"It was disappointing that the SNP government rejected proposals by former Scottish Labour MSP Dr Richard Simpson in the last parliamentary term that would have banned alcohol advertising near schools.
"SNP ministers must get on with the job of refreshing Scotland's alcohol strategy and the recommendations in this report should act as a catalyst for action."