Action Fraid, the national cybercrime reporting centre, said it has received more than 100 reports of scam emails claiming to be from the company in the last month across the country.
The emails vary from notifications about account issues, to promises of free vouchers if the recipient completes a survey.
But the links lead through to malicious websites that are designed to steal Amazon log in details.
But Action Fraud and South Yorkshire Police are warning members of the public to be vigilant and to not fall victim to the scam.
In a statement, police said: “Don't click on links or attachments contained in suspicious emails,
“Don't provide any personal/bank details and contact the company on a known verified number if in doubt.”