Background: Turkey hosts the highest number of refugees in the World including 65% of Syrian refugees who reside in Turkey. Mothers and children were the most negatively affected among the Syrian refugees who had to migrate from their countries as a result of the civil war in Syria. One of the most important issues in terms of child health is breastfeeding. Breastfeeding in migrants should be promoted worldwide to mitigate infant mortality and diseases. The aim of this study is to examine the association between breastfeeding status in Syrian refugee children under two years and socio-demographic characteristics of Syrian refugee mothers with further analysis of Turkey Demographic and Health Survey-Syrian Migrant-2018 (TDHS-SM-2018) data. Methods: The data source is the TDHS-SM-2018. Data for the last-born children with a gestational duration greater than 32 weeks from the mothers’ singleton pregnancy, aged less than two years old and living with the mother were included (unweighted n = 744). The dependent variable was the breastfeeding status (breastfeeding in the last 24 h during the study period) in children under two years. Complex sample logistic regression evaluated the associations. Results: The percentage of breastfeeding in children under the age of two years was found to be 62.4%, and the total median breastfeeding duration was 14.6 months. Univariate analysis showed that the earlier mothers immigrated to Turkey, the higher the current breastfeeding rate. Breastfeeding rates were found to be higher among people living in the South and East regions (65.2% and 65.1% respectively). Multivariable binary complex sample logistic regression revealed that breastfeeding status at the study period was associated with long preceding birth interval; delivery in a public hospital; absence of prelacteal feeding; being non-pregnant; and the region and age of the child. No relationship for current breastfeeding was found with maternal activities, maternal life satisfaction, financial satisfaction, and educational status. Conclusion: Current breastfeeding in our sample was more likely among mothers with a longer birth interval who avoided prelacteal feeding. The Baby-Friendly approach and family planning services should be integrated into refugee health centers.