New England Patriots tight end Aaron Hernandez was sued earlier this month for allegedly shooting a man in the face following an altercation at a Miami strip club ... TMZ has learned.

The lawsuit was filed in federal court in Florida on June 13 -- five days before investigators searched the NFL star's Massachusetts home in connection with a homicide investigation that appears to be unrelated.

According to the lawsuit, obtained by TMZ, Hernandez and Alexander S. Bradley went to Tootsie's Cabaret in Miami on February 13, 2013 ... and during the outing, the two men got into an argument.

Bradley claims ... After the dispute, both men left the club -- and got into the same car which was heading to Palm Beach. During the ride, Aaron allegedly aimed his weapon at Bradley ... and the gun discharged, striking Bradley in the face.

Bradley claims he suffered major injuries from the gunshot ... including the loss of his right eye.

Bradley also claimed he required major surgery to reconstruct his face ... which required plates and screws. Bradley also claims he suffered damage to his right hand and arm, which also required surgery.

There's more -- Bradley claims Aaron was not licensed to carry a firearm in the first place.