If this means that the speaker is married to art in general, "the" is not correct. "The" means that the referenced art is either a specific art or art in some specific work.
I agree completely Dan.
Would the article be correct if, for example, a sculptor was talking about his craft?
we would say, "I'm married to art," rather than saying it's my wife. Married to is a figurative phrase, whereas my wife is very literal.
I disagree, it's a different way of expressing a similar idea. Art is my wife also carries a different meaning than I'm married to art, because it gives art a gender.
What is this sentence supposed to actually mean?
Similarly; 'My wife is no oil painting'....perhaps?