The study carried out by NHS Scotland said there was “anecdotal” evidence of people driving across the Border to stock up on cheaper alcohol to bring home for their family and friends.
Some people living in the south of the country have also started ordering their groceries online from supermarkets on the English side of the Border to take advantage of lower prices, it added.
The policy, which came into force in May last year, makes it illegal for shops, off licences and supermarkets to sell alcohol for less than 50p per unit.
It is supposed to target problem drinkers by making it impossible for shops to sell products such as high-strength cider for knock-down prices.
For the new study, NHS researchers asked licensing standards officers, trading standards officers and police officers for their observations about the policy since it began.
The report concluded that it had generally been well implemented, with most licensed premises such as convenience stores and supermarkets co-operating with the new pricing structure.
However, it said some smaller shops had used the policy as an excuse to raise the prices of all their alcohol, not just products that should be affected by minimum unit pricing.
“A lot of them have used the minimum unit price as an opportunity to just creep up all of their alcohol prices and blame it on Nicola Sturgeon,” one licensing standards officer said.
The study also found that some customers who had previously bought big bottles of high-strength cider had turned to wine instead, given that a 750ml bottle could still be bought for around £4.50.
Some shoppers living near the Border have also changed their behaviour in the wake of the changes.
“Because the point of sale is outwith Scotland, MUP does not apply to these online purchases.”
It added: “Several participants did describe hearing ‘anecdotally’ of people going to stores in England to stock up on alcohol for themselves and or their friends.”
It said there was no evidence that such alcohol was later being re-sold illegally in Scotland, but added: “Several participants did suspect that ‘booze cruises’ were happening.”
Report author Elinor Dickie of NHS Scotland said it was important that the policy was subjected to a “robust and comprehensive evaluation” given that MUP had never been tried elsewhere.
Public Health Minister Joe Fitzpatrick welcomed the report and the fact that researchers had found “no increases in illegal alcohol-related activity” as a result of the policy.