Metal-organic frameworks (MOF) are an attractive class of porous materials due to their immense design space, allowing for application-tailored properties. Properties of interest, such as gas sorption, can be predicted in silico with molecular mechanics simulations. However, the accuracy is limited by the available empirical force field and partial charge estimation scheme. In this work, we train a graph neural network for partial charge prediction via active learning based on Dropout Monte Carlo. We show that active learning significantly reduces the required amount of labeled MOFs to reach a target accuracy. The obtained model generalizes well to different distributions of MOFs and Zeolites. In addition, the uncertainty predictions of Dropout Monte Carlo enable reliable estimation of the mean absolute error for unseen MOFs. This work paves the way towards accurate molecular modeling of MOFs via next-generation potentials with machine learning predicted partial charges, supporting in-silico material design.