Abstract Background In Ethiopia, acute respiratory infections (ARIs) are a leading cause of morbidity and mortality among children under five years. Geographically linked data analysis using nationally representative data is crucial to map spatial patterns of ARIs and identify spatially-varying factors of ARI. Therefore, this study aimed to investigate spatial patterns and spatially-varying factors of ARI in Ethiopia. Methods Secondary data from the Ethiopian Demographic Health Survey (EDHS) of 2005, 2011, and 2016 were used. Kuldorff’s spatial scan statistic using the Bernoulli model was used to identify spatial clusters with high or low ARI. Hot spot analysis was conducted using Getis-OrdGi statistics. Eigenvector spatial filtering regression model was carried out to identify spatial predictors of ARI. Results Acute respiratory infection spatially clustered in 2011 and 2016 surveys year (Moran’s I:-0.011621–0.334486). The magnitude of ARI decreased from 12.6% (95%, CI: 0.113–0.138) in 2005 to 6.6% (95% CI: 0.055–0.077) in 2016. Across the three surveys, clusters with a high prevalence of ARI were observed in the North part of Ethiopia. The spatial regression analysis revealed that the spatial patterns of ARI was significantly associated with using biomass fuel for cooking and children not initiating breastfeeding within 1-hour of birth. This correlation is strong in the Northern and some areas in the Western part of the country. Conclusion Overall there has been a considerable decrease in ARI, but this decline in ARI varied in some regions and districts between surveys. Biomass fuel and early initiation of breastfeeding were independent predictors of ARI. There is a need to prioritize children living in regions and districts with high ARI.