Detective Inspector Craig Hamilton said police were aware that the document was being circulated on social media and warned that distributing it was an illegal activity.
Hamilton, the national manager of the financial crime group, said police were making inquiries to determine how it made its way online.
"This document is Police property and is subject to Section 50 of the Policing Act 2008, and anyone found to have unlawfully distributed it, or found in unlawful possession of it, can be prosecuted," Hamilton said.
No further details were provided about who police were speaking to about the leak.
The police document includes a warning that it can only be distributed internally and is marked "NOT FOR FURTHER DISSEMINATION".
White Rose Society Australia, which describes itself as an anti-fascist research group, said the Telegram channel where the document was published was based in Ukraine.
A mobile phone screenshot of the police memo shows that it was forwarded by a Spark NZ mobile account.
White Rose Society alleged that the police document was published in the same channel where a threat was first made against the Al Noor Mosque in Christchurch last week.
A 19 year-old Christchurch man, Sam Brittenden, was last week charged in relation to that threat.
Hamilton said police regularly provided advice to other agencies regarding the detection and reporting of suspicious activity.
"This advice is always issued with the goal of keeping our communities safe from harm," he said.