The council has issued the warning after receiving a number of reports from residents who have recently been targeted by the scam.
The text messages and emails, sent from random numbers and accounts, claim an unpaid parking fine has been found on the recipient's vehicle and include a link where the recipient can pay the fine "immediately" online.
The link - usually hosted by 'qrco.de', a QR code generator - leads to a convincing copy of an official Government website, which requests personal and payment data from the recipient in order to pay the 'fine'.
But residents have been urged to always check the URL of the website a text message or email links to - as all official Government and council websites and email addresses contain 'gov.uk' in the URL and never 'qrco.de'.
Cllr Claire Edwards, Rugby Borough Council portfolio holder for communities and homes, regulation and safety, said: "The council's parking team never contacts residents or businesses via text message and only makes contact by email - using the address parking@rugby.gov.uk - when replying to a customer's email.
"While the scam website looks official, the text messages and emails expose it's a fake by linking to the site's URL which, in the majority of reported cases, has been hosted by 'qrco.de' - a QR code generator - and not an official 'gov.uk' URL.
"Variations of the parking fine scam messages have been sent to thousands of people across the country in the past few weeks, some claiming to be from local councils and others from the Driver and Vehicle Standards Agency (DVSA), which has never even issued or dealt with parking fines," Cllr Edwards added.
"We're aware of cases where these text messages have been sent to people who do not even drive, so we want to help spread the word about this scam and stop our residents and businesses getting caught out."
Cllr Noreen New, Rugby Borough Council's Liberal Democrat spokesperson for communities and homes, regulation and safety, said: "Everyone needs to remain vigilant when receiving unexpected requests for money, passwords or other personal information and it's best to assume it could be a scam until proven otherwise, so if in doubt, check it out."
For information on how to spot a text, email, website or telephone 'phishing' scam - and how to report it - visit the National Cyber Security Centre website: www.ncsc.gov.uk/collection/phishing-scams/spot-scams
If you believe you have lost money or had a device hacked after engaging with a phishing scam, visit the National Fraud and Cyber Crime Reporting Centre website: www.actionfraud.police.uk/reportscam