NSW Police have charged a Central Coast man over allegedly posting racist comments on the Facebook page of outgoing Northern Territory Labor senator Nova Peris.

Woy Woy-based chiropractor and osteopath Chris Nelson, 64, was arrested at his business yesterday afternoon.

He has been charged with using a carriage service to cause offence.

Nelson has denied he is responsible, saying his account was hacked.

At the time the comments were posted, Nelson was a member of the Liberal Party's NSW division.

A spokesperson for the Liberal Party has confirmed that Nelson has been stripped of party membership over the allegations.

The comments included several instances of profanity.

"You were only endorsed by Juliar because you were a black c***," the comments read.

"Go back to the bush and suck on witchety grubs and yams."

On her own social media accounts, Ms Peris labelled the comments as "racist and vile hatred".

I will continue to call out racism: Peris

In a statement, Ms Peris said racism should never be tolerated.

"I'm sure I share the views of millions of other proud Australians, in that we should pride ourselves on being respectful towards all of our differences as fellow Australians," she said.

"As long as there is racism in any part of society, I will continue to call it out and fight against it.

"No one has the right to make anyone else feel threatened or discriminated against."

The comments drew a strong public reaction after Ms Peris shared them on her own social media.

An online petition calling on police to investigate has attracted thousands of signatures.

The abuse made reference to Senator Peris' Indigenous heritage.

The NSW Chiropractic Council said it was aware of the comments and was investigating.

Nelson will face Gosford Local Court next month.

Last week, Ms Peris announced she would not re-contest her Senate seat at the upcoming election.

She gave an emotional defence of her decision to quit, declaring: "Until you are an Indigenous person, do not criticise me for the decisions I've made".

Ms Peris entered federal politics at the expense of veteran Senator Trish Crossin, who was abruptly dumped by former Prime Minister Julia Gillard in a so-called "captain's pick".

Senator Peris was the first Aboriginal woman in federal politics and Labor's first Aboriginal member in Federal Parliament.

Former Northern Territory MLA Malarndirri McCarthy has been named by the Labor Party to replace Ms Peris.

Ms McCarthy was one of five women who nominated to replace the outgoing Senator, including Ms Peris' chief of staff Ursula Raymond.