No Vaccine Mandates Act of 2021 This bill creates a federal statutory framework to govern restrictions and requirements related to vaccinations. Specifically, the bill prohibits (1) requiring individuals to receive a vaccination that has only received emergency use authorization or received emergency use authorization prior to full approval, or (2) administering such a vaccine to a minor or other individual who lacks the capacity to consent without the consent of a parent or guardian. Additionally, the bill requires a medical provider who administers a COVID-19 vaccination to provide a potential recipient with certain information about the risks associated with the vaccine so the potential recipient can make an informed decision. The bill authorizes civil actions for damages.