My daughter has always been extremely shy and reserved however I enrolled her into gymnastics and I wouldn't let her quit when she said she wanted to because she had given me other clues that she really enjoyed it but she was just too shy. Once she realized that I wasn't going to let her quit is when she started coming out of her shell more. She realized that she was going to have to adjust and that she couldn't just give up and now she can't wait until her next class.
We went through the same kind of thing recently with tball. I almost had to carry her out of the vehicle the first night of tball but at the end of the practice the coach came over and made a big deal out of her being the only girl and it made her feel more comfortable and now she loves it.
You have to find something that you think your child would enjoy and then sign your child up and let the coach know ahead of time what your child is like and most of the coaches will find a way to make your child feel comfortable. I think that the more that a child is exposed to the more independent that child will become and will be able to venture out and try new things.
You may want to start out slowly w/an activity that isn't necessarily a "team sport", something like tennis or golf and gradually work your way into team sports.