Wiltshire Police are warning the public to be wary of messages claiming to be from the NHS and asking the recipient to apply for their vaccine.
The move follows reports in other parts of the country.
A force spokesperson said: "At a time when people are already feeling anxious and eagerly awaiting details of the impending vaccine, scammers are using this to their advantage to commit fraud.
"If you receive such a text, don’t follow the link or share any personal or financial details. The link will take you through to a fake NHS website which is purposefully designed to exploit vulnerable people.
"Fraudsters have tried to use the vaccine as a convincing subject to hook potential victims since the pandemic began. Thankfully reports have been relatively low, however there has been an increase in the last two months.
"The vaccine roll-out brings further hope of fighting coronavirus and keeping people safe. Now that this is imminent and has been so widely covered, some people may be more easily misled.
"You will be contacted by the NHS when you’re invited to receive the vaccine which will be offered in some hospitals, some pharmacies and hundreds of local vaccination centres run by GPs.
"Remember that the vaccine is free of charge, at no point will you be asked for payment details.
Detective Sergeant Sean Tregunna commented: “Although we’ve not been made aware of any cases in Wiltshire yet, it’s likely to only be a matter of time before we are.
"The text message some people have received was shared on social media over the Christmas period and although this does help to raise awareness of the issue, the most vulnerable may not be on social media themselves so we’re asking people to share the information and warn their friends and family.
“The same scam has also been reported as being conducted over the phone. The caller often asks for a number to be pressed on their keypad, resulting in a charge likely being added to their phone bill, so you simply need to hang up.
“We’re keen to prevent as many people falling victim to these scams as possible and urge people to not only share the warning but if they do receive a suspicious text, forward it to 7726 which is free of charge.”
People who believe they have been a victim of fraud are asked to report it to Action Fraud at www.actionfraud.police.uk or call on 0300 123 2040.