Police investigated threats against Pohiva Tu'i'onetoa on Facebook after a member of the public laid a criminal complaint.
But in a statement on Wednesday, police said they spoke to the person involved and found they were "remorseful and meant no harm".
A police spokesperson said threatening a person was a serious crime that could result in prosecution.
"This is true regardless of who is making the threat or what medium they use. Making these threats can cause serious harm to the victims, whether it is acted upon or not."
Chair of the Tonga Advisory Council in Auckland, Melino Maka, who laid the complaint, told RNZ Pacific last month the threat had upset many members of Tonga's community in New Zealand.
However, Mr Maka's claims were questioned by a spokesperson for Tongan political party, PTOA, who was concerned the threat was being linked to the party to drag it through the mud.