Consistent and timely assessments of climate risk are crucial for planning disaster mitigation and adaptation to climate change at the local community level. This article presents an automatized method for assessing climate risk, specially targeting riverine and coastal flooding, at a granular level using machine learning, satellite imagery, and geo-spatial data. Our research posits that risk measures can be more comprehensive and multi-faceted than tracking disasters when they include the following three key components: hazard, exposure, and vulnerability. We first present a model on hazard mapping based on GIS data related to natural hazards, then extend the model to incorporate exposure and vulnerability, where we adopt a clustering-based supervised algorithm to sort satellite images to produce the corresponding climate risk scores at a grid-level. The developed model is tested over a case study on urban flooding risk in Jakarta, Indonesia. Evaluation with multiple ground-truth data reveals that our model can assess climate risk in a granular scale. Regression analysis further shows the applicability of our model by capturing extremely marginalized areas. We discuss how computational methods like ours can support humanitarian projects and international societies by capturing granular climate data in developing countries.