Infants are vulnerable consumers and highly depend on dietary proteins for growth and development during their first months of life. Infant formula (IF) and follow-on formula (FOF) have been developed to meet these requirements, although few protein sources are currently allowed to be used. At the same time, allergies to these available protein sources are becoming more frequent. There is thus a need to explore alternative protein sources for infant nutrition. One alternative could be quinoa, which is a pseudocereal that is naturally free from gluten and has a high protein content and quality. This review assessed the composition, nutritional properties, and applicability of quinoa proteins for IF and FOF as well as the legal framework for their use in the European Union (EU). The protein quality of isolated quinoa proteins (IQPs) is relatively high compared with other plant-based proteins like rice. Besides, during the protein isolation process, unfavorable compounds are mostly removed, ensuring that the final product can comply with the maximum residue concentrations allowed. Overall, IF and FOF are strictly regulated under the Foods for Specific Groups (FSG) Regulation (EU) No 609/2013 and more research is needed before the introduction of IQP in such products is considered, but this review shows it has several promising features that warrant further investigation.