No Coronavirus Copays for Veterans Act This bill prohibits the Department of Veterans Affairs from requiring a co-payment or other cost sharing for qualifying preventive services related to COVID-19 (i.e., coronavirus disease 2019). A qualifying preventive service is intended to prevent or mitigate COVID-19 and is either (1) an evidence-based item or service with an A or B rating in the current recommendations of the U.S. Preventive Services Task Force, or (2) an immunization that has in effect a recommendation from the Advisory Committee on Immunization Practices of the Centers for Disease Control and Prevention with respect to the individual involved. Such a prohibition shall take effect 15 business days after the date on which a recommendation is made regarding a qualifying preventive service related to COVID-19.