It depends on the brand of Worcestershire sauce that you purchase. Lea & Perrins Worcestershire is gluten free. Read your ingredient label. If it does not include malt vinegar, it is gluten free. French's also makes a gluten free Worcestershire Sauce, just make sure to read the label first to ensure you're buying the right one.
Not all Worchestershire sauce is gluten free. The brand Lea & Perrins is a gluten free worchestershire sauce. It is a major and popular brand of sauce and can be found at your local grocery store or super market.