Arrow International, an Auckland-based project delivery company, said its systems had been down all day.
A spokesman said the situation was "pretty messy".
"We've got no computer access at all. It's been terrible."
Steve Voisey, who works in the IT department at Elim Christian College, posted a tweet about the outage at 2:30pm today.
"We're experiencing a major outage at the IBM datacentre at Highbrook. Is anyone else?"
Voisey told nzherald.co.nz that Elim had two campuses in Howick and one of these was completely reliant on the IBM data centre through a service called Nimbus, provided by an IT company called Telco Technology Services (TTS).
Nimbus was designed specifically for New Zealand schools to store their data in the cloud.
"Nimbus increases the safety of your valuable data thanks to it being housed in IBM's $50m state-of-the-art secure data centre in Auckland," TTS said in a brochure.
Freight management firm Kotahi said all online business was stalled today because of the outage.
"We're sort of in a holding pattern right now," a spokesman said.
"IBM's giving us certainty that they're getting their services back up and running."
IBM opened its $80 million, 5200 square metre data centre in May 2011.
The centre allows for companies to securely store and access digital information, removing the need for them to own and maintain computer servers.
On its website, IBM describes the data centre as "a local New Zealand cloud" which was "designed with Kiwi businesses in mind".
"This enterprise-class cloud services delivers a secure and scalable-hosted IT infrastructure with on-demand access to virtual server and storage resources enabling you to create your own virtual data centre."
The building contains a 1500 square metre raised floor, able to hold up to 720 server racks and is kept at an even temperature by 1.4 kilometres of air conditioning pipes.
The server room hooked up to four electricity generators, capable of producing enough juice to power 266 homes.