There is growing concern that climate change will lead to more frequent natural disasters that may adversely affect short- and long-term health outcomes in developing countries. Prior research has primarily focused on the impact of single, large disaster events but very little is known about how small and moderate disasters, which are more typical, affect population health. In this paper, we present one of the first investigations of the impact of small and moderate disasters on childhood morbidity, physical growth, and immunizations by combining household data on over 80,000 children from three waves of the Indian National Family and Health Survey with an international database of natural disasters (EM-DAT). We find that exposure to a natural disaster in the past month increases the likelihood of acute illnesses such as diarrhea, fever, and acute respiratory illness in children under 5 year by 9-18%. Exposure to a disaster in the past year reduces height-for-age and weight-for-age z-scores by 0.12-0.15 units, increases the likelihood of stunting and underweight by 7%, and reduces the likelihood of having full age-appropriate immunization coverage by nearly 18%. We also find that disasters' effects vary significantly by gender, age, and socioeconomic characteristics. Most notably, the adverse effects on growth outcomes are much smaller among boys, infants, and families with more socioeconomic resources.