Inclusion Criteria:
* Pregnant and an estimated gestational age (GA; based on ultrasound dating) from Week 13 to 18 at randomization
* Has a history of greater than or equal to (>=) 1 prior pregnancy with fetal and neonatal alloimmune thrombocytopenia (FNAIT) (including neonatal platelet count less than (<) 150×10^9/Liter) with none of them affected by fetal/neonatal intracranial hemorrhage (ICH) or severe hemorrhage based on medical records
* Current pregnancy with presence of maternal anti- human platelet antigen (HPA)-1a alloantibody and positive fetal HPA-1a genotype as confirmed by cell-free fetal deoxyribonucleic acid (DNA) in maternal blood
* Health status considered stable by the investigator based on physical examination, medical history, vital signs, 12-lead Electrocardiogram (ECG), and clinical laboratory tests performed at screening
* For maternal participant and neonate/infant, willing to forego participation in another clinical study of an investigational therapy until the last follow-up visit
Exclusion Criteria:
* Currently pregnant with multiple gestations (twins or more)
* History of severe preeclampsia in a previous pregnancy
* History of myocardial infarction, unstable ischemic heart disease, or stroke
* Known allergies, hypersensitivity, or intolerance to nipocalimab or its excipients (refer to the Investigator Brochure (IB))
* Has any confirmed or suspected clinical immunodeficiency syndrome or has a family history of congenital or hereditary immunodeficiency unless confirmed absent in the participant