Gastroenteritis and hepatitis, caused by human noroviruses (HuNoVs) and hepatitis A virus (HAV), respectively, are the most common illnesses resulting from the consumption of food contaminated with human enteric viruses. Food-grade polymers can be tailor designed to improve food safety, either as novel food-packaging materials imparting active antimicrobial properties, applied in food contact surfaces to avoid cross-contamination, or as edible coatings to increase fresh produce's shelf life. The incorporation of antimicrobial agents into food-grade polymers can be used to control the food microbiota and even target specific foodborne pathogens to improve microbiological food safety and to enhance food quality. Enteric viruses are responsible for one fifth of acute gastroenteritis cases worldwide and the development of food-grade polymers and biopolymers with antiviral activity for food applications is a topic of increased interest, both for academia and the food industry, even though developments are still limited. This review compiles existing studies in this widely unexplored area and highlights the potential of these developments to improve viral food safety.