The Single Use Carrier Bags Charge Regulations (Northern Ireland) 2013 were approved by the Assembly in January.
The fee will be doubled in April next year, and a charge will also be introduced then for reusable bags.
It is hoped the legislation will reduce the 160m bags issued by shops each year in the region and in turn deter pollution.
The Department of Environment is collecting the levy, which next year is expected to total around £2m. That cash will then be used for environmental projects.
But there has been opposition, and Declan Allison from Friends of the Earth told UTV he believes 5p per bag is not going to have a big impact on consumers.
He said: "It's going to make very little difference on top of the cost of the goods that they're buying."
Mr Allison described the tax as "badly designed", adding Friends of the Earth would rather see a levy of 25-30p introduced.
He continued: "We support levies of this kind in principal, but this one we think won't do the job that it's meant to do."
A similar tax has been in place for some time in the Republic of Ireland, where shoppers currently pay 22 cents per bag.
Meanwhile Ikea started charging for plastic bags almost 10 years ago, and later introduced bags for life, which customers would reuse.
Nigel McGarry from the store said they found it did make an impact on the number of bags customers used.
He added: "We found even with Bags for Life that the take-up was not great and people preferred to fill up their trolleys and take their goods straight to the car."
Local retailers have also voiced their concerns about the impact the levy could have.
Aodhan Connolly from the NI Retail Consortium said: "Our concern is that there may be confusion and possibly conflict at the tills because, although there has been a campaign of communication on this, some consumers won't know and won't understand what the levy is."