In recent months, suggestions have emerged that the ban on alcohol at matches should now be lifted to allow drinks to be sold at stadia.
But the Scottish Collaboration for Public Health Research and Policy says such a move would be a regressive step in the fight against the nation’s alcohol problems.
In a letter published in the Journal of Public Health, they urged football clubs and their governing bodies not to push progress back three decades.
The ban was initially imposed following rioting at the 1980 Scottish Cup final between Rangers and Celtic.
Although alcohol can be served in corporate hospitality areas of football stadiums, the ban applies in every other part of grounds.
In September, the Scottish Football Association (SFA) asked ministers to consider ending the ban, calling for a “serious and robust debate” on the issue.
It came after senior clubs were asked by Scottish Conservative leader Ruth Davidson whether they would back scrapping the ban.
Spectators at rugby matches in Scotland are allowed to drink at grounds
In England, fans at football matches are allowed to consume alcohol before games and during half time, but not in view of the pitch.
In their letter, health experts Tony Robertson, John Frank and Ruth Jepson from the Collaboration said that while they understood why clubs may want to increase revenues through alcohol sales, they felt the voice of the public health community needed to be heard in the debate.
They wrote: “In Scotland, as with many other countries, we face a battle to change our relationship with alcohol.
“Simply put, as a country we consume too much.”
They said to be effective, messages about the harmful consequences of alcohol could not become disjointed.
“Reintroducing the sale of alcohol in Scottish football stadia would be a regressive step in the battle against over-consumption and misuse of alcohol,” the experts added.
“Do we really want children attending football matches to be exposed to even more alcohol advertising and the visible consumption of alcohol?”
Speaking to The Scotsman, Dr Robertson said: “This ban was put in because of violence and hooliganism at the time.
“While it maybe hasn’t had a measurable public health impact, it does seem like a regressive step from the other alcohol policies in place which we hope will have an effect on reducing alcohol consumption across the board.
“It is about the normalisation of alcohol consumption across the board… we need to change our relationship with alcohol.”
A Scottish Government spokesman said: “We are committed to ensuring that football fans can enjoy our national sport in a safe, enjoyable environment.
“Decisions are informed by police and we have no plans at this time to remove the existing restrictions on alcohol at football matches.”