Background Despite numerous interventions, child undernutrition continues as a problem of global concern. Although consumption of animal source foods has shown positive associations with child undernutrition, no much evidence exists on its trends and predictors among children in Tigrai. Objectives This study aimed to investigate the trends in and predictors of consumption of animal source foods among children 6–23 months of age in Tigrai. Methodology This study used complex data of 756 children extracted from three consecutive Ethiopian Demographic and Health Surveys. Data were analyzed using STATA 14.0 by accounting for sampling weight and cluster and strata variables. Multivariable logistic regression was used to determine the independent predictors of animal source foods consumption. Odds ratio and 95% confidence interval were used to measure strength of association at a statistical significance of p < 0.05. Results Although statistically not significant (p-trend = 0.28), animal source foods consumption increased from 31.3% to 2005 through 35.9% in 2011 to 41.5% in 2016. For every month increase in the age of a child, a 9% increment in the odds of animal source food consumption was observed. Muslim children showed 3.1 times higher odds of animal source food consumption than Orthodox Christians. The likelihood of animal source foods consumption were 33% lower among children born to mothers who didn’t attend formal education as compared to their counterparts. A unit increase in the number of household assets and number of livestock led to a 20% and 2% increase in the odds of animal source foods consumption, respectively. Conclusion Animal source foods consumption showed a statistically non-significant increase over the three consecutive Ethiopian Demographic and Health Surveys. This study found out that consumption of animal source foods might be increased through pro-maternal education policies, programs with household asset increasing schemes, and pro-livestock projects. Our study also highlighted the need for considering religion as one important player when planning or undertaking ASF programs.