The government has included the proposal in a range of measures to cut $160 million from the health budget in 2013/14.
It would maintain support for the Quit Line stop smoking service but would end support for other services in schools, workplaces and other groups.
Some services provided to combat drug and alcohol abuse would also be revised.
Health Minister Jack Snelling said the process to identify savings within health was ongoing and consultation would now begin with staff, unions and the broader drug and alcohol service providers.
“I need to be assured that funding is being used in a way that meets the core needs of people using the health system,” Mr Snelling said in a statement on Friday.
But the Cancer Council said a move to cease funding to anti-smoking advertising would have a major impact on smoking rates.
“This is an ill thought out and short sighted decision and given the effectiveness of previous advertising, it will cost lives,” Cancer Council SA chief executive Brenda Wilson said.
“Smokers and the wider public must regularly be reminded of not only the deadly consequences of smoking but also the support and assistance available to those wanting to quit.” Professor Wilson said the proposal also went against the state government’s recent move to sign up to the National Tobacco Strategy in which the states agreed that well funded and sustained mass media campaigns increased quitting and reduced smoking prevalence.
In a separate discussion paper released on Friday the state government also proposed making outdoor eating and drinking areas smoke free.
Under the plan smoking would only be allowed in venues if it was placed in a discreet location, could not be accessed by children and had no food and drink served.
Mr Snelling said banning smoking in alfresco eating and drinking areas would help reduce the number of people affected by second-hand smoke but could also have an impact on the hospitality industry.