Background: In the first 6 months of life, non-exclusive breastfeeding (NEBF) is estimated to be the cause of 1.4 million deaths worldwide and contributes to 10% of the disease burden in under-five children. Aims and Objectives: The objective of the study was to determine the prevalence of NEBF amongst the high-risk children and the factors associated with NEBF. Methods: This cross-sectional study was conducted amongst high-risk babies admitted between August 2016 and February 2018 who also attended the high-risk follow-up clinic at the neonatology department. Data were collected using a pre-tested structured questionnaire. Chi-square test was used to determine the factors associated with NEBF and prevalence ratios (PR) with 95% confidence interval (CI) were calculated. Results: Amongst 304 children, 56.3% were male and 87% had birth weight <2500 g. Nearly three-fourth of the mothers were <30 years of age. The prevalence of NEBF was 49.3% (95% CI: 43.7–55.0). There was a significant association of NEBF with employment status of the mother (PR = 1.45; 95% CI: 1.1–1.9), NEBF in previous child (PR = 2.3; 95% CI: 1.4–3.9) and EBF at the point of discharge (PR = 2.3; 95% CI: 2–2.6). The barriers reported by the mothers leading to NEBF were insufficient or less milk secretion, poor breastfeeding attachment, perceived thirst and poor maternal health. Conclusion: One out of every two children admitted in neonatal intensive care unit were non-exclusively breastfed before 6 months of age. The employment status of mother, practice of exclusively breastfeeding the previous child and EBF at the time of discharge were significantly associated with NEBF.