Amazon said the library has more than 5,000 books and is paying the publishers a fee for the right to lend the books.
However, because that fee is usually the wholesale price of the book, the six biggest publishers, including Random House and Simon & Schuster, are not sharing their books.
They want retail price.
The books cannot be read on phones, PCs or tablet computers, even though there are Kindle apps for those devices.
That restriction is reminiscent of Amazon's strategy of a few years ago, when the company restricted purchased books to being read on Kindles to drive sales of the e-reader devices.
Kindle users recently got access to electronic books from public libraries as well. Those can be read in the Kindle apps.
The Associated Press contributed to this report.