The recommendations, which come less than a month before the minimum age for the purchase of tobacco products rises from 16 to 18, are two of five points outlined in an action plan published by the BMA.
They also include a ban on tobacco vending machines and would help enforce the age increase by reducing availability of cigarettes to young people, the BMA said.
"There is evidence to suggest that the existing age limit regarding tobacco sales is not always properly enforced, which raises questions as to how effectively the age increase will be policed," said Dr Andrew Buist, a member of the BMA's Scottish Council.
"If the new law is to be effective, we need stricter enforcement, supported by a wider strategy to reduce young people's access to tobacco products," he added.
The BMA said that a positive licensing scheme, such as was already in place for alcohol, should be introduced to support the age increase.
"Retailers should be encouraged to stop selling to underage children by the introduction of a licence to sell cigarettes which would be removed for persistent offenders," the report said.
The Association of Convenience Stores said the introduction of such a scheme would be "disproportionate and costly" and would inevitably lead to more red tape for retailers.