Ms Baguley said it had been "progressively recovering" over the past hour and a half, although some customers may still have had trouble texting or calling over that time.
Those in the Wellington area were most effected by the outage, she said.
"The network is still progressively recovering, some customers may still be experiencing some issues but we hope that it will be up and running shortly."
Public information specialist for GeoNet, Caroline Little, said those in the Kaikoura area were sure to have felt today's tremor.
She said this was for "light shaking".
"The deeper the quake, the more rolling the shaking is rather than that violent shaking - they definitely would have felt it."
Ms Little said there were reports of the quake being felt as far south as Timaru, and as far north as Hamilton.
It was likely the quakes were related to two quakes that shook the country yesterday, Ms Little said.
Yesterday's quakes were located east of Seddon, Marlborough, and were widely felt across the strait in Wellington.
The first came at 10.36am and was recorded 20km east of Seddon. It was 23km deep and had a magnitude of 4.4, GeoNet said.
The second hit six minutes later at 10.42am and was recorded 15km east of Seddon. It had a magnitude of 5.1 and was described as strong by GeoNet.
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"I'd say that these are all related in that area and are related to the 2013 quakes as well around the Cook Strait and Seddon area," Ms Little said.
Meanwhile, public information manager for the Kaikoura Civil Defence Rachel Vaughn said the quakes had left those in Kaikoura "scared and shaken up".
"We got two very strong jolts followed by a lot of shaking. We went under our desks and waited for it to stop.
"People were evacuated out of shops but they are going back to business as usual now."
Ms Vaughn said although there had been no reports of damage - it did not mean there was no damage.
"Our engineer has gone to check infrastructure, including sewer and water supplies, making sure our pump stations and everything is working.
"I saw there has been reports of stuff falling off shelves, but no reports of damage."Jacqui Harnett, from Genevieves gift shop in Kaikoura, said the "rumbling" quake had caused things to come off the shelves.
"There was the big one and then there was another smaller one."
"I'm not a good person to talk to about earthquakes because I don't normally feel them. But I couldn't help but feel this one.
"From what I have heard the whole of New Zealand felt it."Ms Harnett said there were only tourists in the town centre at the moment and very few locals.
"The tourists came in and asked us if it was an earthquake because a lot of people from overseas don't get earthquakes," she said.
Minister of Civil Defence Nikki Kaye said the Ministry of Civil Defence and Emergency Management (MCDEM) made contact with a number of local authorities to determine if there were any injuries or damage following the quake.
"At this stage, I am advised that MCDEM hasn't received any reports of major injuries or damage.
"I'm also advised that there are difficulties making contact with some areas, because of communication network issues."
Ms Kaye said MCDEM officials would continue to work to get information from local authorities and other agencies.
"We will advise if there is any significant change to the situation."
