The proposal forms part of a five-point action plan to curb youth smoking in Scotland, which led the UK in banning smoking in public places in March 2006.
The plans, which also include banning the sale of cigarettes in packs of 10 and introducing a licensing scheme for tobacco retailers, were unveiled by Scotland's public health minister Shona Robison last week.
She said: "I am aware that some people will be concerned about further statutory controls on cigarettes. However, I am in no doubt that the prominent display of cigarettes in shops undermines our efforts to shift cultural perceptions of smoking, as does the ease with which cigarettes can be bought.
"Protecting young people from the impact of tobacco must be paramount and there are instances when the benefits to the health of the nation must take precedence."
Abdul Majid, owner of Spar Bellshill in Lanarkshire, said the proposal did not make sense. "The display allows customers to make an informed decision. Cigarettes are not an impulse buy - a customer isn't going to look at the gantry and say 'I like the look of that brand, I'll buy that today'."
Westminster is expected to set out similar proposals when it launches its strategy paper on tobacco in June.
Association of Convenience Stores (ACS) public affairs manager Shane Brennan hit out at the plans, but added that the same laws should be applied to both sides of the border. "While we remain unconvinced of the need for a ban on tobacco displays, the confusion that would be created if Scotland was to implement a different set of regulations to England and Wales would be massive," he said.
Booker chief executive Charles Wilson, who has seen the wholesaler's sales of tobacco to retailers tumble by 6% since the smoking ban, said the proposed measures would have a disastrous impact on sales. "We are investing heavily in non-tobacco areas, as frankly that is where the future is," he added.
The cost of adding new equipment to screen tobacco displays from view could cost the convenience store industry as much as £252m, according to the ACS.