In English, we don't add a comma after "I wonder" because it actually splits the sentence. "What you will do next weekend" is the object of "wonder" - it's the thing that you wonder. Also, since it's not a question, there's no reason to use the inversion that you normally see in English questions. "I wonder what you will do next weekend" is the correct way of writing this statement. Yet is it what you meant to say? Do you want a response from the reader?

Just to add to what Peachy said... "I wonder what you will do next weekend." is a statement. However, it acts like a question and the person you are asking will probably give you an answer. Not necessarily, though. If you meant to ask a true question, it would be "I wonder. What will you do next weekend?" In this case, you are directly looking for an answer.

I wonder what you are going to do next weekend.

I think the correct one is: I was wondering what you will do next weekend.