Facebook has since taken down the post, saying it breached its rules.
A police spokeswoman would not say if other police officers had been targeted in a similar way.
"Police are generally made aware when any staff are targeted on social media. However, it's on a case-by-case basis that we deal with these incidents."
Police asked for the post to be removed.
Netsafe executive director Martin Cocker said doxxing was a common intimidation technique used on the web to make someone feel unsafe.
Doxxing was a breach of privacy, and if people then took action based on the personal information, it could be even more serious, he said.
"Doxxing people is not a fun joke with no consequences - it can cause harm," he said.
A Facebook New Zealand spokesman said the post violated its policies and Facebook removed it as soon as it became aware of it.
Inglis said he was aware of the post and had received emails from people as a result, but could not comment further.
One of the comments on the post showed an email apparently sent to him.
It featured an image of a rifle and the words "come and take it".
It comes less than a month after the deaths of 50 people in the Christchurch terror attacks, and the move to tighten New Zealand's gun laws.
Followers of the US page were encouraged to "mess with" police by falsely filling in gun surrender forms online, something police subsequently criticised in media releases.
The page's moderators said they posted Inglis' details because they were "not fans of gun confinscation [sic], nor those who actively participate in it (especially for a pay check)".
"So as an unofficial protest, trying to get people to peacefully let him know how we feel about his participation in gun confinscation [sic]."
They said they were sent the image of the business card by former Auckland mayoral candidate Adam Holland.
Holland hit the headlines this week after his firearms were seized by police, a move he claimed on Facebook was due to his support for US President Donald Trump.
He posted a photo of a letter from police, signed by Otago-Central Lakes area commander Inspector Olaf Jensen, which said the weapons were being seized due to concerns about Holland's "mental and emotional wellbeing".
He did not respond to a request for comment by deadline.
