Jennie-o Turkey in Coping with Celiac Disease Posted November 25, 2009 · Report to Admin I was wondering if anyone has had a Jennie-O turkey recently or knows if they are gluten-free? It's on the menu tomorrow for Thanksgiving and I've not had much luck surfing their site. It's a regular frozen bird. They have everything else under the sun listed but their frozen poultry. Or I'm blind.