Protecting the Health and Wellness of Babies and Pregnant Women in Custody Act This bill contains provisions related to the medical needs of incarcerated women. The Bureau of Prisons (BOP) shall provide women in its custody access to certain reproductive health services. The bill also requires the BOP to (1) comply with requirements related to the health of a pregnant incarcerated woman, such as providing appropriate meals and medical services; and (2) provide appropriate health care to a woman with a high-risk pregnancy. The bill also modifies restrictions on using restraints on an incarcerated woman during pregnancy, labor, or after delivery. The bill prohibits such restraints unless the relevant corrections official and a health care professional determine that the restraints are appropriate for the woman's medical safety. The health care professional must review this determination every six hours. The current statute allows using such restraints if the corrections official determines that restraints are needed due to a flight risk or threat of harm, and does not require periodic review. The bill also prohibits the BOP from placing a pregnant woman into restrictive housing, such as solitary confinement, unless the relevant corrections official determines that such an action is necessary to address a serious and immediate risk of physical harm. This determination shall be reviewed every four hours. The Department of Justice may make grants to eligible entities, such as a state department of corrections, to provide obstetrical care, gynecological care, and related services to women in custody. The Bureau of Justice Statistics shall collect certain data related to the health needs of pregnant incarcerated women.