The lawsuit filed this week in federal court alleges that the organization, which lends books online for free, amounts to a "piracy site" that has been eluding copyright law for years.
The seven plaintiffs, which include all of the publishing industry's Big Five, say the audiobook company is violating copyrights with a planned feature that would transcribe audiobooks for listeners.
The petition, which comes just before President Obama's historic visit to the island nation, says the embargo is "harmful to book culture" and "counter to American ideals of free expression."