The 49-year-old rap star - who is one of the wealthiest people in the music business - has decided to take legal action against the store in Sydney, Australia, for using his image and lyrics, according to the New York Times newspaper.
It's claimed that the row centres on a book called 'A B to Jay-Z', which re-jigs a line from the rapper's chart-topping hit '99 Problems'.
The reworked line from the record reads: "If you're having alphabet problems I feel bad for your son, I got 99 problems but my ABCs ain't one."
What's more, the book features Jay's likeness, as well as other well-known hip-hop stars like Eminem and the Notorious BIG.
Lawyers acting on behalf of Jay have sent several cease-and-desist letters to the store over the last two years, and they have described the product as a "deliberate and knowing attempt to trade off the reputation and goodwill" of Jay's image.
The legal team also say that the store made a "false and misleading representation" suggesting that Jay had approved of the book.
In response to the dispute, Jessica Chiha, the company's owner, told the New York Post newspaper's Page Six column: "We are unbelievably disappointed to find ourselves caught in a legal battle with someone whose music we love and adore.
"We refer to a whole host of hip-hop artists in the books, but to have someone like Jay-Z file legal proceedings is daunting beyond belief and hugely dispiriting. We maintain we have done nothing wrong and intend to give it everything we've got for common sense and common good to prevail, to the extent we can fight the fight."