If you are a friend, then a quiet, sympathetic chat maybe necessary. If you are just the boss and her self-harming isn't interfering with her work, then I wouldn't enquire. She/he may well be under medical supervision regarding her/his self-harming. It's a tricky one, but there is a lot of stigma surrounding mental health issues and the sufferer could react negatively to any suggestion of self-harming - tread very carefully.
Hmm, would depend if it was recent I think. How do you know they have been?
I self harmed while I was at school/college - if anyone brought it up at work now I'd be mortified, as it was a long time ago at a time when I was desperate.
If it is recent, then I agree with blazingsaddles - it depends on your relationship. If you wouldn't describe yourself as 'friends' then I'd stay out of it, unless there is a problem with their work. Need more info really
Oh, and would also depend on what sort of home life they had, I think - do they have access to other people to talk to outside work etc.