Background: Minimum Acceptable Diet (MAD), developed by the WHO and UNICEF, is a binary indicator of infant and young child feeding practice that assesses the quality and sufficiency of a child’s diet between the ages of 6 and 23 months. Identifying factors associated with MAD among children can inform policymakers to improve children’s nutritional status. Methods: We extracted data of 1930 children aged 6–23 months from the Nepal Multiple Indicator Cluster Survey 2019. Multilevel analysis was performed to identify factors associated with MAD. Results: Only 30.1% of the children received MAD. Children aged 13–18 months [aOR (Adjusted odds ratio): 2.37, 95% CI (95% Confidence Interval): 1.77, 3.17] and 19–23 months (aOR: 2.6, 95% CI: 1.95, 3.47) were more likely to receive MAD than children aged 6–12 months. Early breastfed children (aOR: 1.34, 95% CI: 1.05, 1.72), those currently breastfeeding (aOR: 4.13, 95% CI: 2.21, 7.69) and children without siblings aged under five (aOR: 1.33, 95% CI: 1.03, 1.73) were more likely to receive MAD. Younger maternal age (aOR: 0.97, 95% CI: 0.95–1.0), higher level of mother’s education (aOR: 1.04, 95% CI: 1.0–1.08) and more media exposure among mothers (aOR: 1.66, 95% CI: 1.24, 2.21) were positive predictors of MAD. Relatively disadvantaged ethnicity/caste (aOR: 0.71, 95% CI: 0.53, 0.94), rural residence (aOR: 1.45, 95% CI: 1.06, 2.00) and residing in Madhesh province (aOR: 0.61, 95% CI: 0.37, 1.0) were also significant predictors of MAD. Conclusions: Children aged 6–12 months, without appropriate breastfeeding, having under-five years siblings, with older mother or mother without media exposure or low education, from relatively disadvantaged ethnicity/caste, from urban areas and residing in Madhesh Province were less likely to receive MAD. Our findings can inform infant and young child feeding policies and practices in Nepal.