The voluntary scheme has been introduced at the request of police in an effort to clamp down on antisocial behaviour .
Iceland in Stubbington Green, Crofton One Stop, the Co-op in Upper Old Street and Crofton News & Booze in Gosport Road are among the retailers reported to be on board.
It will run from 6pm on Thursdays through to closing on Sunday and is due to be reviewed after six weeks.
The Wine & Spirit Trade Association has raised concerns that the initiative could breach competition laws.
Chief executive Jeremy Beadles said: "Our view is that there are competition issues when a business knows it is one of a number of businesses doing the same thing, to refuse someone who is legally allowed to buy a product. We have written to Hampshire police asking them to consider this position."
OLN legal correspondent Peter Coulson said the move was probably not illegal. "Shopkeepers have the inbuilt advantage that they can accept or object to sales ," he said. "It's likely to be challenged but they don't have much of a leg to stand on. There's nothing necessarily unlawful about the policy. "