The Ministry of Education is the latest Government department to admit to a privacy breach.
Acting chief executive Peter Hughes said the breach happened on Friday when a Ministry staff member attached the wrong letter to an email.
"It was a simple but very unfortunate case of human error and was quickly identified by the staff member concerned.
"The Ministry takes the privacy of information extremely seriously and I am reminding our staff of the very high level of care needed when handling personal information.
"In the past week we had already disabled the auto-complete address function on emails as a further precaution around emails and will continue to review our processes.''
Mr Hughes said while the letter did not contain detailed information about the child, it was a "deeply regrettable mistake''.
"The letter was advice from the Ministry to the parents advising them that their child could be enrolled at a residential school.
"We visited the family this morning, they have accepted our apology and understood it was human error,'' Mr Hughes said.
"We have also apologised to the unintended recipient of the attachment and asked them to delete it.''
The Ministry has also advised the Office of the Privacy Commissioner about the breach.
This incident comes on the heels of a major breach by the Earthquake Commission which sent details of more than 80,000 claimants to the wrong email address.
The Earthquake Recovery Minister Gerry Brownlee shut down the email system while an investigation was being conducted.
Opposition parties have called for a cross-agency solution to solve the problem of privacy breaches.
Other privacy breaches this year include:
* Immigration New Zealand sent two emails with client email addresses to more than 200 advisers, lawyers and individuals
* EQC sending 83,000 claimant details to the wrong recipient
* EQC also sent a claimant an email with an attached spreadsheet with 2200 names, stopped cheque details and claim amounts worth about $23 million
* The Ministry for the Environment sent about 150 people each other's private email address
* A census collector mistakenly handed out an already complete form to another household
* In January a Hawkes Bay District Health Board worker mistakenly released a patient's confidential medical file to the media;