RxPass will cover doorstep delivery and includes more than 50 generic medications addressing over 80 chronic conditions such as high blood pressure, anxiety, diabetes and male pattern baldness.
But customers enrolled in Medicare, Medicaid or any other government healthcare program will not be able to enroll in the service.
In an interview, Amazon Pharmacy's vice president said the average Prime member would save about $100 per year with RxPass.
The flat $5 charge would be without insurance and on top of the Prime membership fee, which costs $139 a year in the U.S.
Amazon's push into healthcare included the purchase of online pharmacy PillPack in 2018, which helped the retail giant set up a prescription delivery and price-comparison site.
Now, its Pharmacy initiative poses a growing threat to drugstore retailers CVS and Walgreens.
Amazon Prime members in most U.S. states can sign up for the program starting Tuesday.
