Dwayne Walker has sued the star claiming he is owed millions of dollars for his work designing the logo for the rapper's Roc-A-Fella company in 1995.
Jay Z had been expected to give a deposition as part of the legal proceedings, but the hip-hop star's lawyers have now insisted he is too busy to schedule a date for meeting.
In the legal documents, obtained by Tmz.com, the lawyers describe Jay Z's schedule as "gruelling" and state that "preparing a stadium tour is a non-stop effort".
Wayne is seeking $7 million (£4.4 million) from the star as part of the contract and copyright infringement lawsuit. Jay Z's tour with Beyonce kicks off in Miami, Florida on 24 June (14).