It's probably not what you want to hear, but limit the milk. You'll probably get a few tantrums in the process, and it will probably take a few days of reduced milk intake to get her to eat food instead, but if she's getting all of her calories from milk, she's not going to be hungry. You can either give her water instead or if she's really insistent, water down the milk you do offer. I would not offer juice as an alternative, as you'll have the same problem there, and juice has pretty much no nutritional value.
How much milk does she consume on a daily basis, and at what times of day?