The customer and their lawyer received information related to 8000 claims.
Despite the scale of the mistake, Miller characterised the "most disappointing" aspect of the matter as the fact the Government-owned insurer had "multi-layered security measures to protect the information about its customers" and stop it falling into the wrong hands.
EQC moved to fix the error as soon as they became aware and had tried to contain the information.
The lawyer involved had deleted the documents and EQC was awaiting confirmation the customer had done the same.
"We are also contacting all affected customers to apologise to them and explain the steps we have taken to protect their claims information," Miller said.
He said he felt embarrassed and frustrated as his team had worked hard to put new systems and security measures in place after a similar earlier incident.
"Whilst it is difficult to protect any organisation from human error, the incident demonstrates that our systems, processes and training still require further tightening."
A review into EQC's systems had begun with the support of a privacy expert.
"For the past few years, we have been focused on implementing the feedback from our customers to improve our services, so this human error is a massive blow to all our staff who have been working tirelessly to regain the confidence of the New Zealand public," he said.
"Despite this setback we will carry on with our goal of continuous improvement to ensure New Zealand is better prepared for the next major natural disaster."
Any customers with questions were asked to contact EQC on 0800 DAMAGE (326 243).
- RNZ
