Detective Inspector Craig Hamilton, the national manager of the financial crime group, said a woman had been arrested in relation to the unlawful sharing of the document.
She was charged with unlawful possession of police property and will appear in the Wellington District Court on Monday.
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"This material was shared in confidence to financial institutes for the purpose of assisting them with identifying suspicious financial activity.
"Police regularly provides advice to other agencies, including financial institutions, regarding the detection and reporting of suspicious activity."
Inquiries were ongoing and Hamilton said he could not rule out further arrests.
"The advice was issued with the goal of keeping our communities safe from harm, we want our communities to always be safe and feel safe."
As the matter was before the courts, police could not comment further on the matter, Hamilton said.
The police document included 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.
It 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.