Details specific to the New Zealand market will be made available on Friday next week, she said.
A company statement says anyone with concerns over their USB power adapters will be able to drop them off at an Apple shop or authorised dealer for them to be disposed of in an "environmentally friendly way".
A replacement adapter can be bought at the special rate.
"Recent reports have suggested that some counterfeit and third-party adapters may not be designed properly and could result in safety issues," a statement from Apple says.
"While not all third-party adapters have an issue, we are announcing a USB Power Adapter Takeback Program to enable customers to acquire properly designed adapters."