He said the information was released to one person, and he had spoken to them to emphasise it was sent in error and they should destroy the information.
Mr Dunham said he was made aware of the breach on Friday and although it appeared to be a mistake by an individual, the health board would be looking at all its systems to ensure it didn't happen again.
He said he wanted to make sure the systems "challenged" those who were sending information out.
He said it was the first time there had been such a breach.
"It is terrible. We transfer information all the time and have to make sure our systems don't allow it to happen again."
Once an investigation was completed they would report back to the Privacy Commission.
The Ministry of Health is also investigating.
Those with concerns can call 0800 525 371.