You are right to be worried about your niece. I'm not a physician or psychiatrist, of course, but from what you say, it sounds as if she has a very serious eating disorder–so serious that it could be fatal if she doesn't get help. Her parents need to get medical help for her without delay.
Simply urging your niece to eat, or just telling her she isn't fat probably won't solve her problem. No, her idea about herself is not logical–but deep-seated emotional problems seldom are. In other words, her failure to eat properly is really a symptom of a much deeper emotional problem–and she'll probably need help to deal with it. Your doctor or pastor should know what resources are available in her community to help her.
Pray for your niece, and do all you can to let her know you love her. Down inside, she apparently hates the way she is (or the way she thinks she is)–but you don't hate her, and she needs to know that.
More than that, God loves her, and He doesn't want to see her harm herself. God loves her so much that Christ was willing to go to the cross and die for her. The Bible says, "This is how we know what love is: Jesus Christ laid down his life for us" (1 John 3:16). When she understands this truth, it will help put her on the road to recovery.