Protecting Military Installations and Ranges Act of 2021 This bill places restrictions on the purchase of certain property by a foreign person who is owned or controlled by, is acting for or on behalf of, or receives subsidies from Russia, China, Iran, or North Korea. Specifically, the Committee on Foreign Investment in the United States must review a purchase or lease by, or a concession to, any such foreign person of private or public real estate in the United States that is within (1) 100 miles of a military installation; or (2) 50 miles of a military training route, special use airspace, a controlled firing area, or a military operations area. Further, the Department of Defense and the Department of Transportation may not issue final determinations regarding specified projects (e.g., energy projects) that involve a transaction under review by the committee until the committee concludes its action.