Background To eliminate measles, which is a devastating contagious disease, Ethiopia introduced the measles-containing second dose vaccine (MCV2) that will be given in the second year of life. Despite its paramount benefit, the coverage was low worldwide and, in Ethiopia, there is scarce evidence on the geographic variations and factors associated with uptake of MCV2. Objective This study aimed to explore the spatial variations and the individual and contextual factors of uptake of measles-containing second dose vaccine among children aged 24 to 35 months in Ethiopia. Methods We used the 2019 Ethiopian Mini Demographic and Health Survey data. A total weighted sample of 800 children aged 24 to 35 months was used. Multilevel analysis was employed and an adjusted odds ratio (AOR) with a 95% confidence interval (CI) was reported. Factors with a p-value<0.05 in the multivariable analysis were declared to be significant predictors of MCV2 uptake. To explore the spatial variations of MCV2 uptake, we have conducted spatial analysis using both Arc GIS version 10.7 and SaTScan version 9.6 software. Results The proportion of MCV2 uptake was 9.84% (95% CI: 7.96%, 12.11%). Children whose mothers were aged 20–34 years (AOR = 0.19; 95%CI: 0.05, 0.69) and 35–49 years (AOR = 0.21; 95%CI: 0.04, 0.90), being the 4^th-5^th child (AOR = 4.02; 95%CI: 1.45, 11.14) and 6^th and above child (AOR = 4.12; 95%CI: 1.42, 13.05) and children who did not receive full childhood vaccinations (AOR = 0.44; 95%CI: 0.25, 0.77) were significantly associated with MCV2 uptake. Besides, MCV2 uptake was clustered in Ethiopia (Global Moran’s I = 0.074, p-value <0.01). The primary cluster spatial window was detected in the Benishangul-Gumuz region with LLR = 10.05 and p = 0.011. Conclusion The uptake of MCV2 in Ethiopia was low. Maternal age, birth order, and uptake of the other basic vaccines were associated with MCV2 uptake. Besides, MCV2 uptake was clustered in Ethiopia and the primary cluster spatial window was located in the Benishangul-Gumuz region. Therefore, special concern should be given to regions with lower MCV2 uptake such as the Benishangul-Gumuz region. Besides, it is better to give attention to basic vaccination programs.