SHE TOUCHED THE QUEEN!!! IT'S A BREACH OF PROTOCOL!!!!1!!!1!!!!!!!

From USA Today:

Update at 11:25 a.m. ET: A spokesman for Buckingham Palace tells Inside Edition that "it's obvious that it was a mutual sign of affection and appreciated between the queen and Michelle Obama. There is no offense. The reception was an informal occasion. There's no breach of protocol."

So: no, it isn't.