A report by NHS Shetland has suggested the move, in a bid to curb excessive drinking.
About three-quarters of all alcohol consumed in Scotland is now bought from supermarkets or off licences.
The proposal will be considered by the local licensing board after the council elections next year.
Elizabeth Robinson, one of the report authors from NHS Shetland, told BBC Scotland: "People with alcohol problems have told us that they can go out the next morning and buy alcohol at 10am.
"If there was just a bit of a longer break until some time in the afternoon that would really help them.
"You can buy your 14 units a week for about Â£3 in Shetland.
"People tend to pour larger drinks at home."
However, shopkeeper Jordan Thomason said: "I think such a drastic increase in time runs the risk of people buying too much alcohol and then it could have the opposite effect of what they are trying to do."
A proposal that supermarkets and off licences should only be able to sell alcohol later in the day is to be considered in Shetland.