The ban began this week, however there will be a transition period where existing stocks must be used by 1 June.
Plastic shopping bags litter roadsides, add to excess rubbish in the community, and provide breeding grounds for mosquitoes.
To combat that the government has imposed a Prohibition Order after receiving Cabinet approval in February.
The Chamber of Commerce has taken the lead in response to the ban by placing signs outside the main shopping areas, encouraging people to use cloth or re-usable shopping bags.