The US billionaire is suing retailer The Little Homie for knowingly infringing on his trademarks and misleading conduct, including selling the book "AB to Jay-Z".
The conduct is "flagrant, glaring and contumelious", court documents filed in the Federal Court of Victoria last week show.
The online retailer raised $8000 on Kickstarter to publish a picture book called "AB to Jay-Z", which refers to well-known rap musicians to teach the alphabet.
In his suit, Jay-Z, legally named Shawn Carter, claims the retailer knowingly attempted to trade off his reputation and breached copyright of lyrics in the hit song 99 Problems.
The back of the book includes the quote "If you're having alphabet problems I feel bad for you son, I got 99 problems but my ABCs ain't one".
Jay-Z's song famously opened with "If you're having girl problems, I feel bad for you son, I got 99 problems but a bitch ain't one."
The retailer and its director Jessica Chiha are listed as respondents in the case.
Documents show Jay-Z's legal team believe the company and Ms Chiha "are deliberately and knowingly using the intellectual property of Mr Carter for their own commercial gain".
The lawyers said the retailer and director deliberately and knowingly attempted to trade off the reputation of the rapper, who is married to Beyonce.
Using the Jay-Z name, image and wording "calculated to injure, has injured and is continuing to injure the reputation and goodwill of Mr Carter", according to the documents.
The company was asked to stop selling products in March 2018 and despite exchanges with the rapper's lawyers there was no resolution.
Lawyers for Jay-Z and The Little Homie have been contacted for comment.