Is there wheat or gluten in wine?

Yes it can have gluten in it. Do a google search on gluten and red wine and you will see that lately gluten has been used as a clarifying agent in red wines. It used to be animal proteins but because of "mad cow disease", believe it or not, wine makers have started using wheat gluten as an alternative.

Also many wine producers age their wines in wood barrels. These barrels are often pre-treated with a wheat-flour paste on the insides to prevent leakage. Of course this paste has gluten in it which will contaminate the wines.

So, you need to do some research to make sure the red or white wine you buy is not contaminated with gluten.