Non-invasive prenatal testing (NIPT) appeals to the general obstetrical population due to its reliability and safety in fetal aneuploidy screening. However, it often attracts ethical concerns when offered via publicly funded healthcare systems. Using moral reasoning, this paper makes rule utilitarian arguments to address the ethical question: How can NIPT be ethically offered to the general obstetric population via a public healthcare system for the detection of fetal aneuploidy? Three moral arguments were constructed deductively, upon which three governing “rules” are based. According to rule utilitarianism, policies that consider and conform to these rules should lead to maximization of utility for the greatest number of people. This paper provides a moral foundation for formulating policies that govern the roles of NIPT in fetal aneuploidy screening programs and may, therefore, have implications for many people, including pregnant women, the disabled, and society as a whole.