Ronda Rousey is so tough, she BROKE HER FINGER on the set of the "9-1-1" TV show -- BUT NEVER BROKE CHARACTER!!!

Ronda -- who plays an L.A. Fire Dept. badass on the show -- was shooting a scene in Mexico last week in which she was supposed to slam a door during a dramatic action moment.

But, as one source put it ... "She was a little over-exuberant and slammed the door on her finger."

We're told Ronda didn't wince, didn't complain, didn't mess up the scene ... instead, she continued to stay in character and finished the scene.

Only after the director yelled "cut," we're told, Ronda FINALLY acknowledged the injury -- saying, "Ow. You're not gonna like this!"

Ronda went to a doctor who diagnosed her with a broken finger -- which is NOTHING for the former UFC superstar.

She got a splint for her hand and went right back to work the next day, our sources tell us.

Hollywood ... it ain't for the weak.