The correct sentence is this:
"He is out of the office."
This is a full sentence indicating that the person in question is not present in the office where he usually works. There are some nouns of place - such as 'school', 'work' and 'home' - which can be used in a full sentence without an article. 'Office' is not one of these nouns - you have to say 'the office', 'this office', 'my office' and so on. It is not possible to omit the article in the sentence above.
The set phrase 'out of office' is sometimes used as an adjective. For example, when you sign out of your email or go on leave you might leave an 'out of office message' as an automatic reply. This is the only context in which you would usually see 'out of office' without the article.