We have some friends with a little girl with the same problem. I think it falls into the category of social anxiety disorder. Hers certainly did. Read these links and see if you don't agree. The first link is information from a pediatric psychiatrist named Dr. Jim Chandler, who's written a good bit on this topic:
http://www.klis.com/chandler/pamphle...obpamphlet.htm
Social Anxiety Disorder (This is just some good general info and further links.)

I personally feel that the worst thing in the world would be to force her to play on a team. That'd just make the anxiety worse and add to the pressure she already feels, most likely making her feel more anxious about social/sports situations and possibly adding new injury to the level of safety, comfort and trust she has with you, her parents.

Dr. Chandler talks about two approaches to dealing with the problem, behavioral and medicinal. I think people often go the medicinal route far too quickly with kids and jump right to the pill-based approach, which, if you ask me, ought to be the last resort rather than the first. The behavioral approach wouldn't be as easy or fast as a pill, but it would probably help her face those fears under safe, therapeutic circumstances and seems like it'd be worth seriously considering. Our friends ultimately went the medicinal route with their child after some initial behavioral work, and the combination of the two approaches helped their daughter but certainly hasn't eliminated her shyness or anxiety. It's more manageable now, however, and she's not paralyzed by her fear in the same way that she was. That's a rough thing for kids and it can be crippling for some of them. My heart goes out to you and your little one!