Jimmy Fallon's Jager-Bombed Hand Is All Good

Jimmy Fallon's going to run out of fingers to injure at this pace ... but he doesn't seem the least bit rattled after cutting his right hand on a shattered bottle of booze.

Jimmy posted a shot of the his bandaged right index finger, saying ... "Nothing that a few band aids couldn't fix."

TMZ broke the story ... Jimmy was partying with the Harvard Lampoon crew Saturday night, and carrying a bottle of Jägermeister, when he tripped over someone. It sounded bad, but Jimmy seems unfazed ... especially when compared to his more horrific left hand injury.