“who art in heaven” is a grammatical relative clause because the subject of the verb is the relative pronoun “who” which is second person in that context. You can still get this kind of thing in modern English, for example “I, who am a farmer, will be happy” is grammatical because the relative pronoun “who” is first person there. That doesn’t mean it would be grammatical to say “*A farmer am happy” and it wouldn’t have worked with art either.

Conceivably it’s grammatical if Henry is vocative and the pronoun is dropped colloquially, like “Who art [thou], O Henry?” but it’s a stretch.