Blogger Keith Ng says he was able to download 7,000 files from the department's network using a public computer in a Work and Income New Zealand office made available for job hunters.
Included in the files were names of children currently in state care, Ng said.
The files, which also included the names of people suspected of benefit fraud, were easily retrievable "by just using the open-file dialogue on Microsoft Office," Ng wrote in a blog.
He was also able to access children's medical records, legal bills and debt collector invoices, the BBC reported Monday.
Ministry officials said they had shut down all of the computer "kiosks" in its public offices and there was no evidence the network had been hacked.
"I apologize to everyone now," Social Development Minister Paula Bennett told Radio New Zealand. "I'm mortified that they had that level of trust in the ministry and at some level we've let them down."
Ng said he handed over all the files he downloaded to the ministry and did not keep copies.
"This stuff was all a few clicks away at any WINZ kiosk, anywhere in the country. The privacy breach is massive, and the safety of vulnerable children was put at risk," he said.
"This should never have happened."