We have the same issue with our 5 year old, but stopped making a big deal out of it as we felt that we were encouraging her to do this by noticing.  Also, we figured it was better than her doing this to someone else.

skye started to do this also same age but now has escallated to hitting out she was always a quite girl who was calm but now she is the most demonstrous little girl going and has a really bad way of showing her anger/frustration, we now have to sturnly say no or even result to naughty chair/time out this doesnt always work and is one of those things i dont like going through as its all new to me, i only worry that she will turn out to a little madam like me!!!! that s bad, all i can say is divert her attention when she goes to start doing this, but it is hard and am quite reliefed im not the only one going through it, we could always swap children if you like!!!!

Have you tried to show her other ways to release her frustration?  Like jumping up and down or coloring?  We have to teach them how to properly handle their emotions, counting is a good way as well.  When you see her getting frustrated, instead of saying don't bite yourself it not right, instead tell her, I know your frustrated, here lets count to 20 to calm down.  It will take time, but once you find a way to help her redirect her frustration and help her thru it, she will start to do it on her own.  I'm working with my girl to stop the screaming that she likes to do and to try and do something else that will help her calm herself down....Hang in there!