Background: Down syndrome is the most frequent genetic cause of intellectual disability, with an estimated birth prevalence of 14 per 10,000 live births. In Brazil, statistical data on the occurrence of babies born with Down syndrome remain unclear. We aimed to estimate the occurrence of Down syndrome between 2012 and 2018, and to observe its association with maternal, gestational, paternal characteristics, and newborn vitality. Methods: A retrospective study was carried out using secondary data included in the Certificate of Live Birth in a state located in the southeastern region of Brazil. Data analysis was performed in the software Stata 14.1. Pearson’s chi-square test for bivariate analysis, and logistic regression for multivariate analysis were performed, with a 95% confidence interval (CI) and a significance of 5%. Results: We observed that 157 cases of Down syndrome were reported among 386,571 live births, representing an incidence of 4 in 10,000 live births. Down syndrome was associated with maternal age ≥ 35 years, paternal age ≥ 30 years, the performance of six or more prenatal consultations, prematurity, and low birth weight (p < 0.05). Conclusions: Women aged 35 and over were more likely to have children born with Down syndrome. In addition, there is an association of Down syndrome with premature birth, low birth weight, and the number of prenatal consultations (≥6).