A Wairarapa woman was arrested on suspicion of inciting racial disharmony after a hateful message was posted to her Facebook page in response to the Christchurch shootings.

The offence falls under the Human Rights Act and carries a maximum penalty of three months' imprisonment or a $7000 fine.

Police say a decision is still to be made about whether the woman will be charged and put before the court, or face an alternative resolution.

The Times-Age believes the woman is a parent to a child at a Masterton primary school, and parents complained to the principal and the police.

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Senior Sergeant Jennifer Hansen said the Facebook post "upset a number of people because it referred to the events in Christchurch".

She said the post was brought down relatively quickly, but not before "a number of people had already seen it and raised concerns".

The woman is believed to be in her late 20s.

A charge of inciting racial disharmony can be laid against a person who "publishes or distributes written matter which is threatening, abusive, or insulting" to other people, on the grounds of colour, race, ethnicity or national origins.

On Monday, an 18-year-old accused of sharing a live-stream of the Christchurch mosque mass shooting was refused bail.

The teen faces two charges: one of sharing the gunman's live-stream and a second for posting a photograph of one of the mosque's attacked with the message "target acquired" along with other chat messages "inciting extreme violence".

The 18-year-old appeared in Christchurch District Court today and was granted name suppression. However, his request for bail was refused by Judge Stephen O'Driscoll.

Police have said the teen - who cannot yet be named - was not involved in the shootings on Friday.

He is due back in court next month.

The charge relating to distributing an objectionable publication is dated March 15, the day of the mosque shootings, court documents show.