Public Health Minister, Maree Todd, said she found the current levels of alcohol advertising "deeply troubling" and wanted to reduce the attractiveness of alcohol.
Ms Todd said a consultation on a number of proposals would take place in the autumn.
She also said an uplift in the minimum unit price of alcohol was "attractive", but "robust" data on how the policy had worked so far was needed to do this.
The minister spoke to MSPs at Holyrood's Health Committee on Tuesday.
She said: "We know that there is a direct link between exposure to alcohol marketing and children and young people drinking alcohol, and this can increase the likelihood that they will drink in ways that can be risky or harmful in later life.
"I personally find this deeply troubling and I'm determined to cut down on the volume of alcohol advertising and promotion that young people see."
She continued: "I also hope I can count on support from across Parliament to tackle the harmful impact of alcohol marketing when the consultation launches."
The minister noted that alcohol-related deaths increased during the pandemic, but the average levels of alcohol people were drinking was reducing.
Those who drank heavily before the pandemic drank even more heavily after the onset of coronavirus, she said.
SNP MSP, David Torrance, asked about the Government's plans for minimum unit pricing.
Ms Todd said any change would need to have a "robust evidence base".