Evidence on the impact of the quality of prenatal care on childhood mortality is limited in developing countries, including India. Therefore, using nationally representative data from the latest round of the National Family Health Survey (2015–16), this study examined the impact of the quality of prenatal care on neonatal and infant mortality in India using a multivariable binary logistic regression model. The effect of the essential components of prenatal care services on neonatal and infant mortality were also investigated. The results indicate that improvement in the quality of prenatal care is associated with a decrease in neonatal (OR: 0.93, 95% CI: 0.91–0.97) and infant (OR: 0.94, 95% CI: 0.92–0.96) mortality in India. Tetanus toxoid vaccination, consumption of iron–folic acid tablets during pregnancy and having been weighed during pregnancy were statistically associated with a lower risk of neonatal and infant mortality. Educating women on pregnancy complications was also associated with a lower risk of neonatal mortality. No effect of blood pressure examination, blood test and examination of the abdomen during pregnancy were found on either of the two indicators of childhood mortality. Although the coverage of prenatal care has increased dramatically in India, the quality of prenatal care is still an area of concern. There is therefore a need to ensure high-quality prenatal care in India.