When you start a sentence with "I wonder," you're making a declaration about your state of mind. Because it's a declaration, it's a not a question, so don't use a question mark.
WRONG: I wonder how he is?
RIGHT: I wonder how he is.
Think of it this way:
JACK: Is there a God?
JILL: I wonder.
JACK: You wonder what?
JILL: I wonder whether there's a God, silly.
Jill's just declaring her state of mind. It would have made no sense to punctuate either of her lines with a question mark.