The Game picked the wrong guy to sock in the mouth during a basketball game ... TMZ has learned his victim is an LAPD officer.
Law enforcement sources tell us the guy who got into it with the rapper during the hoops game over the weekend is a rookie cop ... who was off-duty at the time.
It's interesting -- as TMZ first reported ... Game is saying the guy threatened him before the fight by hinting he was going to get a gun out of his gym bag. For his part, the punchee told responding officers Game is the one who issued a death threat. Our Game sources say he denies that.
We're told LAPD is investigating the Game for battery -- and also the off-duty officer. If he really did threaten to get his gun ... he could be in big trouble.