We developed a cloud microphysics parameterization for the icosahedral nonhydrostatic modeling framework (ICON) model based on physics-informed machine learning (ML). By training our ML model on high-resolution simulation data, we enhance the representation of cloud microphysics in Earth system models (ESMs) compared to traditional parameterization schemes, in particular by considering the influence of high-resolution dynamics that are not resolved in coarse ESMs. We run a global, kilometer-scale ICON simulation with a one-moment cloud microphysics scheme, the complex graupel scheme, to generate 12 days of training data. Our ML approach combines a microphysics trigger classifier and a regression model. The microphysics trigger classifier identifies the grid cells where changes due to the cloud microphysical parameterization are expected. In those, the workflow continues by calling the regression model and additionally includes physical constraints for mass positivity and water mass conservation to ensure physical consistency. The microphysics trigger classifier achieves an F1 score of 0.93 on classifying unseen grid cells. The regression model reaches an $ {R}^2 $ score of 0.72 averaged over all seven microphysical tendencies on simulated days used for validation only. This results in a combined offline performance of 0.78. Using explainability techniques, we explored the correlations between input and output features, finding a strong alignment with the graupel scheme and, hence, physical understanding of cloud microphysical processes. This parameterization provides the foundation to advance the representation of cloud microphysical processes in climate models with ML, leading to more accurate climate projections and improved comprehension of the Earth’s climate system.