She said a case manager had agreed to listen to voicemail messages she had saved from the man, but never came.
The 67-year-old described the ordeal as "horrible".
"He said he knew where I lived and said I had a nice face," she told the Dominion Post.
She told ACC the man gave his name as "Brian or Byron", and had indicated he lived in Petone.
ACC told the Dominion Post it had been aware of the matter since April 2010, and it was being investigated by the commission and police.
"Further, matters of privacy are currently under investigation by the Office of the Auditor-General and the board of ACC, in conjunction with the privacy commissioner.
"These investigations are examining ACC's privacy processes and its governance," the paper reported ACC as saying.
The incident is the latest controversy in a string of privacy breaches ACC is accused of.
ACC client Bronwyn Pullar received the details of about 6,500 clients, including the victims of sexual abuse, in an email last year.
On March 23, Canterbury student Stacey Parenti received another woman's claim in the mail instead of her own.
- Herald Online staff