But rather than showing how much the individual had contributed, the emails showed zero contributions had been made for the year in bolded type.
The email also stated it was an estimate only that may be different to the actual contributions made.
One woman who contacted the Herald said she expected people would be annoyed at the email.
"ASB has mistakenly sent this out to their customers and I think people will be a bit annoyed that the bank is stating we haven't contributed enough for the Government subsidy."
Another woman said her son received the email and she had automatically assumed it was a phishing scam because she knew he had contributed $5000 over the year.
Her son called the ASB fraud hotline to report it but was told the email was legitimate but had been sent to him in error.
An ASB spokeswoman said a message was sent earlier today to around 200,000 KiwiSaver Scheme customers to remind them of the upcoming deadline to receive their full KiwiSaver annual Government contribution.
"Unfortunately, an error with our automated messaging system meant customers who have either already contributed sufficiently to maximise the Government contribution or are on track to do so ahead of the June 30 deadline, received this message."
She said the bank was contacting customers today to notify them of the error.
"We apologise for the confusion this has caused and want to reassure our ASB KiwiSaver Scheme customers that this was purely a communication error.
"Our records of their KiwiSaver account contributions over the past 12 months are correct, and their KiwiSaver balances are accurately recorded."
ASB is the second largest KiwiSaver provider and manages more than $14 billion on behalf of members.
The total KiwiSaver market is worth around $87b.