MOTLEY CRUE singer VINCE NEIL got so upset at a "fan" in the front row during a solo concert in New Mexico LAST weekend that he THREW A PUNCH at the guy from the stage.

He was performing "Kickstart My Heart", when he suddenly stopped to yell, quote, "Get the [eff] out of here!" at a guy in the front row.

Apparently, the guy said something back . . . because Vince got so worked up that he took a swing at him.  The guy ducked out of the way, and Vince missed.

TMZ claims Vince was upset because the guy "repeatedly tried to grab at him" while he was performing . . . but there's no official word on what was going on.

That SEEMED to be the end of it . . . security came over and booted the guy, and Vince went on with the show as if nothing had happened.  But supposedly, this "fan" attempted to return for more face-time with Vince.

A rep for the venue says, quote, "During the post-performance party at the property, the intoxicated fan and his group of friends, who were also visibly inebriated, returned and continually attempted to get close to Vince."

One report said the guy and his friends were "hell-bent on revenge" . . . so they probably weren't coming back to smooth things over.  Fortunately for Vince . . . or perhaps the "fan" . . . he never got through security.

Vince hasn't talked about the incident directly . . . but on Saturday, he Tweeted, quote, "FYI:  If you're a hater, please stop following me and Motley!!  We don't care about you!  Hopefully Goodbye!! :)"