The lawsuit, filed Thursday in Manhattan Federal Court, accuses Ortiz of naming his Santo Domingo club Forty-Forty in the hopes of trading in on the rap star's fame.
The suit seeks over $5 million in damages and for Ortiz to forfeit any use of the 40/40 name.
Jay-Z's string of bars can be found in Manhattan, Las Vegas and Atlantic City.
"David Ortiz is fully aware of Plaintiff's Manhattan 40/40 club, since he had been a patron there on several occasions before he opened his Infringing Forty/Forty club," the lawsuit states.
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.