To evaluate rates of breast milk feeding among infants with cleft lip with or without cleft palate (CL ± P) enrolled in Medicaid compared to Private Insurance/Self-Pay. This was a population-based retrospective cohort study. The 2018 US National Vital Statistics System—Natality component (NVSS-N) was used to examine nationwide birth certificate data. Infants with cleft lip with or without cleft palate and either Medicaid or Private Insurance/Self-Pay were included. Breast milk feeding rates among infants with CL ± P, as a function of insurance status. Chi-square tests of independence revealed that of 896 infants with CL ± P and insured by Medicaid, 527 (58.8%) were breast milk fed at discharge. Of 865 infants with CL ± P and insured by Private Insurance/Self-Pay, 621 (71.8%) were breast milk fed at discharge. Using logistic regression models and controlling for baseline demographic differences, results indicated that infants with CL ± P in the Medicaid group had reduced odds of breast milk feeding compared to the Private Insurance/Self-Pay group (OR = 0.08; 95% CI 0.56, 0.96). Breast milk support services are often necessary for the initiation of breast milk feeding among infants with CL ± P. However, these resources are likely not as readily available for those enrolled in Medicaid. These results suggest that infants with CL ± P, enrolled in Medicaid, may experience reduced breast milk feeding rates due to limited resources to initiate breast milk feeding. Factors that may promote breast milk feeding among this population are discussed.