Reserve Bank deputy governor Christian Hawkesby said systems related to Anti-Money Laundering and Countering Financing of Terrorism (AML/CFT) laws must be correctly designed and implemented.
"We appreciate that design errors can occur," Hawkesby added.
He said prescribed transaction reports were important for building intelligence about New Zealand's financial system.
"Unfortunately, these coding errors compromised the quality of the information held by the FIU."
Hawkesby said BNZ had worked hard to fix the issue and provide the police unit with the right information.
The Reserve Bank said the rebuke should remind other entities of obligations under AML/CFT law.
BNZ is not the first major bank to receive a warning.
In August last year, the Reserve Bank formally warned Westpac for failing to comply with anti-money laundering rules.
The central bank said Westpac's internal systems failed to detect and report almost 8000 corporate transactions to overseas recipients between July 2018 and February 2019.
Westpac at the time identified an inadvertent mistake with a reporting system as the cause of the error.
The law required financial service providers to report all overseas transactions worth more than $1000 to Police and the Reserve Bank.