They are several pictures of Madonna sucking her thumb, in fact
in her biography told by a very close friend, she mentions some
thumb sucking activity of Madonna in her early years teens and
early 20´s, mostly to get attention but also as part of her
childhood habit. I am not sure she still does this, although I can
assure she was a thumbsucker until her 30´s. There is also an
unofficial video while making the video VOgue, where she is sucking
her thumb during the breaks. So, hey, why not ask her, maybe she
still does.