Retailers must now charge shoppers at least five pence for each new single-use carrier bag.
The proceeds of the tax will be forwarded to the Department of the Environment.
The department hopes to see an 80% reduction in the use of carrier bags as a result of the levy.
The tax also applies to bags made from paper, plant-based material, or natural starch.
The regulations also allow for a range of exemptions on the grounds of hygiene and food safety, the protection of goods and consumers, and confidentiality in respect of bags for medicines.
Environment minister Alex Attwood said he believed "the vast majority of people" would be happy with the introduction of the new levy and realised that plastic bags and single use bags were a "threat to our environment".
"If we have a wonderful, clean and green country in the north of Ireland, let's protect it," he added.
"I think most people will see the benefit of this and most people will embrace this new proposal."
Mr Attwood said the money raised from the levy would be deployed across Northern Ireland "in a fair way".
The British Retail Consortium's Aodhan Connolly said that, while his organisation did believe the tax would have an impact "our line would be that there are bigger environmental fish out there to fry".
"Our biggest concern is that maybe there's going to be some confusion or even some conflict at the tills," he said.
"Although there's been a lot of communication about this there seem to be a few consumers out there not quite ready for it yet.
"What we're really talking about here is a culture change and for that to happen it's going to take quite a while to embed, all we're asking for is a bit of patience."
Wales was the first UK nation to introduce a plastic bag tax - doing so in 2011.
Scotland is currently considering such a move. There is no bag tax in England.
The new levy on plastic carrier bags has come into effect in Northern Ireland.