No Meddling in American Elections Act of 2021 This bill establishes a new criminal offense involving the public disclosure of false information by a federal officer or employee. Specifically, the bill prohibits the public disclosure of false information by a federal officer or employee (1) in any manner prejudicial to the safety or interest of the United States or for the benefit of any foreign government to the detriment of the United States, except with the approval of the President; or (2) for the purpose of influencing a federal election. A violation is punishable by a statutory maximum prison term of 10 years.