Leigh Day claims thousands of drivers could be entitled to an average of £10,500 compensation for each year they have delivered for the company.
Because drivers are classified as self-employed, they do not benefit from rights such as holiday pay and an employment contract, the law firm said.
It added that at least 3,000 drivers could be able to claim for employee rights.
Kate Robinson of Leigh Day said: “Amazon is short-changing drivers making deliveries on their behalf. This is disgraceful behaviour from a company that makes billions of pounds a year.
“Drivers delivering for Amazon have to work set shifts and book time off, yet Amazon claim they are self-employed.”
A spokesman for Amazon said: “We’re hugely proud of the drivers who work with our partners across the country, getting our customers what they want, when they want, wherever they are.
“We are committed to ensuring these drivers are fairly compensated by the delivery companies they work with and are treated with respect, and this is reflected by the positive feedback we hear from drivers every day.”