She may have overactive sweat glands that make her palms really damp and uncomfortable.
She may be reacting to stress with this as an unthinking way of comforting herself, like a younger kid would automatically suck a thumb for comfort (have there been changes at home, changes at school, issues with friends?)
She may feel a compulsion to do this repetitive action; does she do other things that seem repetitive or like little rituals she needs to do before moving on to other things?
She may have a mineral deficiency that she's totally unaware of, of course, and having discovered that the saltiness of the sweat seems satisfying, she's doing this licking, when she may really need something else that's dietary.
With her right now, I wouldn't freak out, yell or discipline her; I wouldn't even mention it to her until after you talk to her pediatrician, which I'd do right away. This could be a temporary tic or it could be an indicator of the kinds of things above, all of which can be handled medically. Of course it's a worrying habit, with flu season upon us and who knows what other germs running around school, but if you punish her for it or shout at her, that may backfire and make her lick more, for comfort. So I'd definitely talk to the doctor soon and maybe to the school counselor (if you have a well-trained and trusted counselor). And keep the lines of communication with her open; if you're gentle and positive with her, she's likelier to tell you about why she feels she needs to do this.