Background Pneumonia is the leading cause of mortality and morbidity in under-five children. Regardless of this fact, efforts to identify determinants of pneumonia have been limited in the study area. The aim of this study was to identify determinants of community-acquired pneumonia among 2–59 months of age children in Northeast Ethiopia. Methods Facility-based unmatched case-control study was conducted from February to April, 2019 among 444 (148 cases and 296 controls) 2–59 months of age children in Northeast Ethiopia. Cases were children with pneumonia, while controls were non-pneumonia children. Data were collected using a structured and pre-tested questionnaire by integrated management of neonatal and childhood illness trained nurses. The data were entered into Epi Data and then transferred to SPSS version 23 for analysis. Binary logistic regression analysis was used to test associations between the independent and the dependent variables. Variables with P-value ≤ 0.05 in the multivariable logistic regression model were declared as significant variables. Results Children having older age mother (AOR = 0.03, 95% CI; 0.01,0.14), having mothers who are housewife (AOR = 0.19, 95% CI; 0.07,0.54), not having separate kitchen (AOR = 5.37; 95% CI: 1.65,17.43), having a history of diarrhea in the last 2 weeks (AOR = 10.2; 95% CI: 5.13, 20.18), having a history of acute lower respiratory infection in the last 2 weeks (AOR = 8.3, 95% CI: 3.32, 20.55) and having a history of parental asthma in the family (AOR = 4.9, 95% CI: 2.42, 10.18) were found to be determinants of community-acquired pneumonia. Conclusions Children having older age mother, having mothers who are housewife, not having separate kitchen, having a history of diarrhea in the last 2 weeks, having a history of acute lower respiratory infection in the last 2 weeks and having a history of parental asthma in the family were found to be determinants of community-acquired pneumonia. Therefore, all health institutions should promote early treatments and prevention of diarrhea and acute lower respiratory infections of under-five children at the health facility and household level.