Several conditions related to serious difficulty in initiating and maintaining breastfeeding in neonates with Down syndrome are described in the literature. This study aimed to investigate the frequency of breastfeeding in neonates with Down syndrome, as well as the reasons for not breastfeeding, through a systematic literature review by searching MEDLINE via PubMed, Cochrane Library, Scopus, Embase via Elsevier, and Cumulative Index to Nursing and Allied Health Literature (CINAHL) databases. Sixteen studies were included with a total sample size of 2022 children with Down syndrome. The frequency of exclusive breastfeeding was 31.6-55.4%, with five studies reporting breastfeeding for longer than 6 months. Breastfeeding from birth was present for 48-92.5% of the children with Down syndrome in six studies. Two studies reported that around 50% and 23.3% of the children with Down syndrome were never breastfed, and rates of breastfeeding in infants with Down syndrome were lower than those in controls in three studies. The reasons for not breastfeeding or cessation of breastfeeding were associated with Down syndrome-specific challenges, maternal reasons, and healthcare aspects.