Federal Correctional Facilities COVID-19 Response Act This bill requires federal correctional facilities to provide COVID-19 tests at no cost to inmates and employees and otherwise addresses the management of COVID-19 in these facilities. Correctional facilities operated by the Bureau of Prisons (BOP) and private facilities that house inmates under contract with federal entities must provide initial tests within 15 days of the enactment of this bill and also establish a weekly testing program that will remain in effect through the end of the COVID-19 pandemic. Inmates may opt out of this testing. In addition, facilities must provide appropriate follow-up services for those who test positive for, or display symptoms of, COVID-19, including necessary medical care for inmates and access to paid leave for employees. Furthermore, each facility must report specified COVID-19 data to the Department of Justice (DOJ), the Centers for Disease Control and Prevention (CDC), and the public health authority of the state in which the facility is located. Specifically, facilities must report COVID-19 outbreaks to the CDC, and the CDC must deploy staff to facilities with outbreaks to prevent further spread of the disease. The bill also applies certain federal privacy standards for health records to, and restricts the use of, any data collected as a result of the testing and reporting activities. Additionally, the BOP, in consultation with the CDC and other experts, must update certain guidelines on managing COVID-19, and DOJ must also report to Congress on COVID-19 prevention, mitigation, and control activities at federal correctional facilities.