The Harry Potter franchise forever changed the way adults, and children themselves, think about reading appropriateness. With so many very young children taking on Harry during his years at Hogwarts, either by themselves or by being read to, there's now an expectation that all blockbuster fiction is okay to take on as well. Which brings me to The Hunger Games.
The Hunger Games. I would never discourage a child from reading, but this is a series that firmly belongs in very mature 'Tween and Teen territory. A big tip-off is that book is not shelved in the Children's Room; you'll find it in Teen Fiction. Truly, it is not the best choice for young readers; even advanced young readers. If nothing else, it takes a more mature mind to comprehend the brutality of a society that forces its children to kill each other.
Since the release of the movie (which is rated PG-13), interest in the book series has of course only increased. Here's a great review about the film from Common Sense Media.
That said, there are several classic must reads about dystopian societies for kids and a great place to start is Lois Lowry's The Giver, Gathering Blue, and Messenger. After reading these, they'll appreciate The Hunger Games all the more when they are ready for it, and may the odds really truly be ever in their favor.