The scam, which is circulating by text and email, offers the recipient the chance to book a coronavirus vaccine and includes a link to a fake NHS website.
Police say if you have received these messages to not click on any links and delete them immediately.
The genuine vaccine is free of charge so any approaches or adverts for a vaccine in return for payment are highly likely to be a scam.
Police are also urging everyone to be very cautious of any website or communication which asks for personal and/or bank details and advise never to click or follow any links in a text message or email.
The best way to find information from GOV.UK, or any other agency, is to visit that particular website via a trusted search engine, such as Google.
A spokesperson for the Force said: "We have also received reports of cold callers using the same approach to offer the vaccine in return for payment. This is a scam. If you receive one of these calls, hang up immediately.
"Unfortunately, this is yet another example of how scammers are using the Covid-19 pandemic to target people and prey on their fears.
"If you think you have been the victim of a scam then please report this to North Yorkshire Police by calling 101."