Detective Shaun McClintock said this week he did not want to reveal how many people had been scammed or how much they had lost, because his investigations were continuing.
However, he agreed several people meant "between one and five" people who had responded to offers "for a ridiculously low price" and the public needed to be warned about the risks.
Social media scams were common in New Zealand, with fraudsters targeting community bulletins, discussion forums and trading sites, Det McClintock said.
"They are not specifically targeting Wānaka, but every market group," he said.
However, his investigation was just on behalf of the Wānaka complainants, Det McClintock said.
He had received complaints about other social media scams, which around Christmas usually involved people buying or offering to sell Christmas presents, Det McClintock said.
People who believed they had been scammed should not feel ashamed and should talk to the police, he said.
"Fraudsters are smart and some have been doing it for a very long time. It is possible to find out who the main culprits are but it can be impossible too," he said.
