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.
Spark has more than 250 Wi-Fi phoneboxes throughout Auckland and anyone within range, including non-Spark customers, can search for "Spark wi-fi zone" and join the network, with no password required.
Spark WiFi zones can be viewed online at www.spark.co.nz/getmore/freewifi.
Vodafone says its network is "faring well" although a number of sites are down throughout the wider Auckland area.
"Generators are being distributed by technicians to the Mangere Bridge and Onehunga areas, where customers may have seen some degraded cellphone coverage."
2degrees says its network has "come through the storm well".
"We have no reports of damage but obviously power is an issue," a spokesman said.
"We have a number of sites across the Auckland region that are either running on battery power or are down completely as a result of the storm. Predominantly these are in the west of the city and our technicians are working with both fibre network providers and electricity providers to bring these back up as quickly as possible."
Meanwhile Chorus says its copper and fibre networks "largely operating as usual" across the country despite the storm.
In Auckland and Taranaki there have been power outage issues and some cabinets and exchanges re running on battery back-up systems or generators to keep cellphone and radio sites running.
About 6000 households and businesses are without phone or broadband service.
A Chorus spokesman said its service companies had increased the number of technicians available so they can deal with outages as quickly as possible but it would only access sites if it was safe to do so.
"Technicians will prioritise medical escalations as they are raised by retail phone and broadband providers."
Vodafone has also confirmed that more than 80 Auckland areas have been affected by the storm.
The company's website says repairs are ongoing.