Among those affected was Camberley resident Katarina Houia who woke with a fright at 1.30am after hearing her father's phone from the other end of the house.
She didn't realise what the noise was until her father, after the third text, told her he'd received the alerts and turned his phone down.
Vodafone customer Amy Crysell, who lives in Puketapu, said she was a little tired after receiving three messages at 1.32am, 1.33am and 1.49am.
"The idea behind the message is great," she said.
"But the test messages, three of them sent in quick succession, at that time in the morning is a little ridiculous.
"I understand civil emergencies happen at any time but this was a test. The waking hours would have been much better."
A Napier resident, who did not want to be named, said she was unhappy to be woken by three loud, buzzing, high pitch alerts.
"It wasn't so fun when you've just come out of surgery."
However, Jervoistown resident Maxine Matthews said she was pleased to have received the texts.
"I was happy that if it was real I would have woken up and got my family up the hill.
"I love the work Civil Defence is putting in to try and save lives and I'm happy to participate in any further testing."
Ministry of Civil Defence & Emergency Management director Sarah Stuart-Black said the messages were sent in error between 1.30am and 1.50am and while they only affected Vodafone customers the mistake was not the phone company's.
"The Ministry accepts full responsibility and are seeking assurances from our service provider to make sure it doesn't happen again."
The alerts were sent by a provider based in Europe and was only meant to be sent to a select testing group.
"There was something in the system that hadn't restricted it to just in that testing environment so it went to the wider public," she said.
"We offer our sincere apologies to those people who were awoken or inconvenienced by these messages."
"Don't worry if you're a Vodafone customer and you didn't get the alert - not all phones are Cell Broadcast enabled."
The noise made by the alerts was also much louder then an ordinary text message sound.
Emergency Mobile Alerts will be rolled out in November to provide Cell Broadcast text alerts in emergencies.
