Pregnant Women Health and Safety Act of 2021 This bill establishes requirements for physicians who perform abortions and abortion clinics. Specifically, the bill requires a physician who performs an abortion (1) to have admitting privileges at a nearby hospital; and (2) at the time of the abortion, to notify the patient of the hospital location where the patient can receive follow-up care if complications arise. A physician who fails to comply is subject to criminal penalties—a fine, a prison term of up to two years, or both. A woman who undergoes an abortion may not be prosecuted. The bill also requires an abortion clinic, in order to receive federal funds or assistance, to (1) be licensed by the state in which it is located, and (2) be in compliance with federal standards for ambulatory surgical centers.