Spark NZ says the storm has cut power to its cellphone tower network, affecting broadband.
The telco says its network is not damaged, but 50 of its cellphone towers around the country are offline because of power cuts, and a number of others are running on battery power.
It is using generators as a backup.
"As the majority of the affected cellphone towers are in the greater Auckland area, customers may still receive some mobile coverage from other cellphone towers in their area. However, customers may experience slower than usual mobile data connections as the load increases on the remaining towers," the company said.
Because of the number of towers offline, it has opened its Wi-Fi network to anyone who needs it.