Masks for All Act of 2020 This bill requires state, tribal, territorial, and local governments to mandate, as a condition of receiving federal COVID-19 (i.e., coronavirus disease 2019) relief funds, the use of face coverings in public spaces during the COVID-19 emergency. The bill also provides for exceptions to this requirement, such as for individuals who are under the age of two and those who need assistance removing face coverings. In addition, the Department of Health and Human Services may award grants to states, tribes, and territories to promote access to face coverings, including by installing face covering dispensers in public places.