The lawsuit, filed Thursday in Manhattan Federal Court, accuses Ortiz of calling his Santo Domingo club Forty-Forty in the hopes of trading on the rap star's fame.
Jay-Z's string of bars can be found in Manhattan, Las Vegas and Atlantic City.
Lawyer Peter Raymond tells the New York Daily News that Ortiz had visited the clubs twice and certainly knew about them.
The clubs are named after the feat of hitting 40 homers and stealing 40 bases in one season.
A message seeking comment was left Thursday night with SFX Baseball, the agency that represents Ortiz.
