The boxer behind the lawsuit is Daniel Franco -- who claims he signed a deal with Roc Nation Sports back in 2015 ... and won his first 5 fights with Jay-Z's company.

But, the problems started in March 2017 ... Franco claims he came down with a bad flu before a big fight which sidelined him from training for 3 weeks.

Franco claims he told Roc Nation he needed to postpone or cancel the March 23 fight -- but Roc Nation pressured him into fighting anyway.

Franco says he lost badly in the 3rd round and should have taken time off to recover ... but instead, Roc Nation booked him to fight again 50 days later on May 12.

Then, Franco claims Roc Nation booked him for a third fight just a month later on June 10 ... his third fight in 79 days.

But, Franco claims Roc Nation never took the steps to make sure he was medically fit to take that third fight ... and it could have cost him his life.

In the court documents, Franco claims he believes he suffered 2 skull fractures and a brain bleed before the June 10 fight that could have been detected.

Instead, Franco says he fought on June 10 -- and lost again -- suffering major damage in the process.

Franco claims he was diagnosed with a brain hemorrhage and went into a coma. Doctors needed to remove a piece of his skull to relieve pressure from the bleed.

After 2 weeks, Franco awoke from his coma but claims he still has severe neurological and cognitive issues ... and is required to wear a helmet at all times to protect his brain.

In his suit, Franco says Roc Nation and Jay-Z had a duty to protect him -- but instead acted recklessly by scheduling him to fight 3 times in 79 days without "necessary medical testing."

He's asking for unspecified damages.