It is an important story and, taught properly in the classroom, can be a good study for fourth grade.  But your question is asking for opinions and hopefully more people will chime in with theirs.
 
Mine is "yes" - that the book (properly taught and handled in the classroom) is appropriate for 4th grade.  I do think, however, that it would work better in 5th grade or later.
 
I asked my 11-year-old (5th grade) daughter this question and her answer was, "Yes, if the kid is somewhat mature, knows something about World War II, and takes things seriously.  It is a sad but serious book."

The school systems have taken pains in the last decade to reform reading requirements to include topics that students can emotionally connect with. One of the biggest debates since the 90's has been about Reading history books of facts, or factual books about history. When a student reads The Diary of Anne Frank in high school, it is used to augment a history lesson. When a 9 year old reads it, they are at a cognitive stage where they can understand that the holocaust was bad, but they are begining to develop the capacity to think critically about it. Reading the personal story of Anne Frank is a great way to have young children feel a connection to a piece of history, while they learn to digest the socio-polictical implications of the time.