My daughter did this. Actually, she voluntarily gave up her binkie and immediately replaced it with her thumb. Unfortunately, I don't have a solution. Binkie fairy finally came after she stopped sucking on her thumb at all times except to sleep. Here are my thoughts:
1.) Honestly, I would have preferred that she continue with her pacifier instead of her thumb or fingers. At least the pacifier can be sanitized before it goes in her mouth and I could control when she got it. With her thumb, she is in control of when it goes in the mouth... dirty hands and all.
2.) I had to make peace with the realization that she is going to suck on something in order to get to sleep. Granted she is probably sucking on her thumb MUCH LESS than when she used a pacifier (because the thumb moves out of the mouth eventually while she is sleeping, although usually I move it if she has it in her mouth when I check on her). And she is no longer thumb sucking in the car when tired (that's progress!). However, yes I could buy thumbs guard to stop her from sucking her thumb... but if it isn't her binkie or thumb, then she would probably be sucking on her fingers, hair, blanket, lovey, etc. If she is determined to suck something, I absolutely do not want her developing the habit of sucking on clothes, bedding and hair! Decide what your poison is... Mothers who I work with all told me that their children eventually gave up thumb sucking. She won't do it forever.
Good luck.