While child undernutrition has been eliminated in some middle-income countries, it remains highly prevalent in sub-Sahara African (SSA) and South Asian regions, and is disproportionately concentrated among the poor. In this study, we estimated trends in child undernutrition by social determinants and related risks from wealth inequality in Ethiopia, from 2005 to 2016. We analyzed data from three consecutive surveys (2005, 2011, and 2016) from the Ethiopian Demographic and Health Survey. First, we estimated trends in the prevalence of childhood undernutrition variables (stunting, underweight, and wasting) and social determinants (household wealth status, education level, place of residence, and administrative regions). Then we assessed evidence of undernutrition by wealth-related inequality with concentration curves (visual) and concentration indeces (quantitative). A multilevel mixed-effect Poisson regression model was used to identify predictors of undernutrition variables expressed as covariate-adjusted rate ratios, with 95% confidence intervals (RRs, 95%CI). A total of 23,934 mother-child pairs were obtained from the three surveys. The average prevalence decreased by 12.4 percentage points for stunting (from 50.8 to 38.4%, P<0.01), 9.5 percentage points for underweight (33.2% to23.7%, P<0.01), and 2.1 percentage points for wasting (12.2% to10.1%, P<0.01). There was persistent and statistically evidence of wealth inequality in stunting, underweight, and wasting (concentration indeces of -0.2 to -0.04, all P values <0.05). Stunting, underweight, and wasting variables were associated with male sex of the child (RR 0.94, 0.95, 0.85, all P-values <0.01) recent diarrhea (RR 1.18, 1.27, 1.37, all P-values <0.01), secondary education status of the mother (RR 0.66, 0.57, 0.61, all P-values < 0.057), increasing wealth index (richest) (RR 0.73, 0.70, 0.50, all P-values < 0.05), and having no toilet facility (RR 1.16, 1.22, 1.18, all P-values < 0.05). Despite the decreased burden of stunting and underweight, the prevalence of wasting remained relatively unchanged in Ethiopia from 2005 to 2016. Moreover, wealth-related inequality in child undernutrition increased for most of the child undernutrition indicators during this period. Social determinants of child undernutrition warrant urgent implementation of strategies to reduce their health impacts in SSA.