The website does not contain any comparison information but asks users to fill out a form with their personal details so a third party can contact them, the FMA said.
The warning came amid a surge in complaints from investment scam victims.
The FMA said victims entered personal details into comparison websites and were then contacted by individuals purporting to be from well-known banking institutions such as Citibank or HSBC.
“Some victims have lost hundreds of thousands of dollars to these schemes,” the FMA added.
CFTD’s website indicates it was based in Australia.
But according to the FMA, both the Australian and New Zealand Companies Offices and financial regulators found no record of CFTD.
“We believe this website is a front used to harvest personal information from New Zealanders for criminals to exploit,” the FMA’s Paul Gregory said.
“The FMA strongly encourages New Zealanders to only deal with locally-registered entities and if someone is pushing you into an investment opportunity, step back and ask yourself: why am I being offered this over the phone?”
He urged people not to be feel rushed, but to be sceptical and ask lots of questions.
“Hit the pause button before sending or committing any of your money to people you cannot truly verify,” Gregory added.
“Most often with scams like these, your money is transferred overseas and it is incredibly difficult for New Zealand authorities to get back.”
The FMA said since June, it had received 154 complaints about investment scams and fraud, and issued 40 public warnings about scams and other non-compliant entities.
Dodgy sites were often presented alongside legitimate comparison sites and appear as “sponsored” links, rather than genuine search results, the FMA said.
The authority urged people to check carefully before sending any money or personal information to an investment opportunity.
“Do not trust links, emails or contact details supplied by callers. Check for yourself with the institution.”
The warning follows a spate of other scams surfacing or resurfacing recently, including a fake police text scam.