Question mark when ending sentence with "I wonder"?

Both are correct English.

The first sentence has an embedded question object complement of a mental perception verb, and, as described here, sentences like these are often intoned as questions, because they're intended as requests for information. When a writer wishes their sentence to sound like a question in the mind's ear of the reader, they use a question mark; otherwise, not. This is very ordinary.

The second sentence has undergone a Dislocation, wherein the embedded question is moved to the front of the sentence, presenting a question form and signalling a bald request for information. And therefore, it is almost always punctuated with a question mark in writing; this is also very ordinary.

I wonder why that is. Is a question asked in a manner not expecting any answer in response. It is in it's own way telling the answer.

Whereas Why is that, I wonder? is asked to have a answer in response, that's why we use a question mark over here.

A quick survey of Google Books reveals that in both forms are commonly written with, and without a question mark.

Without a question mark, both forms become a statement of fact.

I wonder why that is.

Why is that, I wonder.

You can imagine them spoken with a downward inflection on the last syllable.

With a question mark, they are questions, perhaps rhetorical, but you can imagine them being spoken with an upward inflection, as if inviting an answer.

I wonder why that is?

Why is that, I wonder?

If you phrased your sentence,

I wonder, why is that?

it would require a question mark as well. The distinction is not where "I wonder" occurs, but the subject-verb inversion in "why is that"/"why that is". Subject-verb inversion is the grammatical way to form questions using the "wh" words which, why, how, who, what, and where. Grammatically, your first sentence is a statement.