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The 27-year-old woman had contacted the union member, who was a Facebook acquaintance, over an issue she was facing with an employee.
They met for coffee and during the meeting, the staff member allegedly asked her for a hug.
When she refused, the woman said the staffer appeared annoyed but she didn't think much of it then.
However, she later received a text, purportedly from a union member saying: "If you want me to settle your this matter or any other comes in future I told you lets meet you give me favour I will look after rest [sic]".
The woman asked: "What favour you talking about?"
He replied: "Why you act like you innocent? I know your kind of girls book a room I will be there and don't worry about other things. Else I will contact all your employees and talk to them and will take you to labour department as you are exploiter."
The union's boss confirmed the union has had a complaint "raising an allegation of a very serious nature against one of our employees".
"We have kept the complainant regularly informed."
He also would not say if suspension was standard procedure.
"We can make no other comment on this while the investigation is under way in accordance with required practice in terms of procedural fairness in such employment matters," the union's boss added.
Minister for Workplace Relations and Safety Andrew Little said he too was unable to comment on the allegation.
But he said workplace harassment and bullying is never okay.
"Every New Zealander deserves to feel safe in the workplace, and every complaint must be treated with sensitivity and care," Little said.
"The Government will continue to progress options in this space to combat bullying and harassment in our workplaces."
The woman, whom the Herald is choosing not to name, said she contacted the union member after an employee had made a complaint against her.
"I thought he could give me advice about what to do, and I was shocked when he asked me to book a room to have sex with him," she said.
"I am quite a conservative person, so I was just stunned at his request."
The woman believed the union worker carried out some of his threats after she refused his requests.
"He rubbished my reputation online, contacted my staff and suppliers saying bad things about me and destroyed my credibility," she said.
The woman said although the initial contact and text message exchange were in late 2018, the harassment had continued.
She said that she "couldn't take it any more" and filed a complaint with the union staff on July 10.
"I have been suffering from depression because of this in the past two years, I've had to wind up my businesses and I'm also not in a mental state to work," the woman said.
The suspended union staff member denied any wrongdoing and said the woman's complaint were "all lies".
"She made up fake chats and set me up and I have gone to the police about her," he said.
"My lawyers are also handling the matter."
When approached, a police spokeswoman said police "cannot respond to queries which seek to establish whether a specific individual or organisation is, or has been, under police investigation".