J.N.
It's most likely a phase. Some kids are naturally comfortable performing, others aren't. But, just like stranger anxiety, almost all kids go through a phase of stage fright.
If it's something that she really wants to do, but is scared, give her support and encouragement. Tell her that everyone, even very experienced performers, get nervous before a performance, and that it kind of keeps them on their toes. (I play with an orchestra, have on and off since high school, and still get nervous every time, especially if I have even the tiniest solo).
If it's something she's not so into, don't push it. If it is something like a ballet recital, and her whole class is going to be doing it, encourage her to give it a try, but if she backs out at the last minute, let her know it is okay, she can try again next time (and ever notice how many little girls in their first ballet recital freeze up or run off the stage? very normal). Just don't push her into it if she's not ready, it'll likely increase the anxiety for the next time!