You can't break up and her not be hurt. Sorry but that is part of life. What you can do is be as kind as possible. You talk to her face to face. Let her know that even though you care for her, you are not in love and it isn't fair to either of you to continue on with the relationship.
How do I break up with my girlfriend without hurting her because she is very emotionally fragile. (I'm also a girl)?
Face to face, in a public place, be honest.
Maybe if you try and put yourself in her position it would help. How would you want to be broken up with? What words would make you feel less hurt?
You would need to make sure she still feels good about herself and that she is a good person and you'd like to remain friends if possible, but that you don't see a future with her as far as dating.
Don't let her emotions get the best of you and keep you from breaking up with her or she will just use that over and over. You need to be sure of your decision and STICK TO IT or else it's not fair to either one of you.
It will all work out okay soon enough and she will be fine. It's nice of you to care about her feelings and she will be okay. The world is full of broken hearts that went on to find someone else. Good luck and just do your best.
Part of life is learning to deal with disappointment. If you feel your relationship isn't right for you ... It's much wiser for you and kinder for her if you don't continue in your relationship. If she is emotionally fragile, that's very sad .. But she has to deal with that. You can't feel bound to someone because they are "fragile". You can be kind to her .. But honest. If you break up .. You both will have a chance at the future happiness you both deserve. Good Luck.