New York Rangers -- Fan Hit By Puck Sues ... I'm Permanently Injured

11:50 AM PT -- We spoke with Cantor's lawyer who tells us ... the 59-year-old man was at the game with his son when he reached out with his hand to block the puck from hitting his kid's face.

We're told Cantor was struck in the left thumb -- leaving him with significant damage to his thumb, hand and shoulder ... damage which required surgery to repair.

A hockey fan who says he was hit by a puck at a NY Rangers game is suing the team -- claiming he was permanently injured during a 2013 game ... TMZ Sports has learned.

The man behind the suit is Robert Cantor -- who claims he was in the stands at Madison Square Garden on March 3, 2013 to watch the Rangers play the Sabres when things went terribly wrong.

In his suit, filed in state court in NY, Cantor claims he was "struck by a high speed projectile (puck) and [sustained] severe and permanent injuries."

Cantor says he suffered pain, shock and mental anguish and is unable to perform normal activities.