Gluten-Free is on the menu, but the same kitchen also prepares what you avoid, so cross-contamination is possible. Tell staff what you react to, and ask how your dish is prepared before you order.
A traditional Viennese inn in Leopoldstadt, open on weekdays. It keeps a separate gluten free card with breaded schnitzel, cordon bleu, goulash and desserts, and the site says most dishes can also be made gluten free. Gluten free beer is on the card.