Public Health Emergency Production Act of 2021 This bill modifies funding, administration, and reporting related to the Defense Production Act of 1950. That act confers upon the President a broad set of authorities to influence domestic industry to secure essential materials and goods needed for the national defense. Specifically, the bill eliminates a requirement to transfer any balance in excess of $750 million from the Defense Production Act Fund to the General Fund of the Department of the Treasury. In addition, the Department of Health and Human Services (HHS) must require companies to prioritize fulfilling federal contracts or orders necessary for pandemic preparedness and response if HHS finds that the material being procured is essential to the public health and cannot be adequately sourced through normal distribution channels. HHS must also establish, within the Office of the Assistant Secretary for Preparedness and Response, an office responsible for Defense Production Act of 1950 activities. Additionally, staff may rotate between the Office of the Deputy Assistant Secretary of Defense for Industrial Policy and specified components of HHS. Furthermore, the Defense Production Act Committee must report monthly about the use of Defense Production Act of 1950 authorities during the COVID-19 (i.e., coronavirus disease 2019) emergency.