In Afghanistan, acute respiratory infection (ARI) is a leading cause of under-five mortality. Previous studies on the effects of cooking fuel on ARI have only looked at the types of cooking fuel, and not the effects of the location of the cooking place. The present study aimed to assess the effects of fuel type and place of cooking on the prevalence of ARI among under-five children in Afghanistan. Descriptive statistics and multilevel logistic regression analysis were performed for 31,063 children using data from the first round of the Afghanistan Demographic and Health Survey conducted in 2015. Overall, 13% of the children suffered from ARI symptoms in the 2 weeks before the survey, but this varied widely across the country. The multilevel analysis showed that, compared with households using clean cooking fuel in a separate building or outside, households using clean cooking fuel within the house and without a separate kitchen had a 32% lower risk [95% confidence interval (CI)=0.51–0.91] of having under-five children with ARI, and those using clean fuel in a separate kitchen in the house had a 17% lower risk (95% CI=0.67–1.03). On the other hand, households using polluting cooking fuel in the house without a kitchen had a 14% (95% CI=0.91–1.44) higher risk of having under-five children with ARI, and those using polluting cooking fuel in the house with a separate kitchen had a 5% (95% CI=0.85–1.30) higher risk, after adjusting for other covariates. The findings indicate that type of cooking fuel is not the only issue affecting ARI in children. Place of cooking (in a house with or without a separate kitchen versus outside) also affects the risk of ARI among under-five children. The study also found that mother’s education and occupational status, community poverty and ethnicity are other important factors affecting the prevalence of ARI in under-five children in Afghanistan.