Parenthetical double negation?

Solution 1:

The sentence reads correctly, but a bit clumsily because legally and physically are not bound. By that I mean, the negation makes sense, but I have trouble immediately understanding what you're referring to with "legally, not physically." You might consider:

He cannot go outside (legally speaking, but not physically), because he is on house arrest.

Solution 2:

Because the term house arrest already provides a great deal of context, it probably isn't even necessary to include the word physically. Perhaps try rephrasing with something like:

Legally, he is not permitted to go outside because he is on house arrest.

Solution 3:

In legalese typically shall not is used. It avoids the ambiguity of the word can. May not would also seem to be appropriate.