Permeability of fibrous microstructures is a key material property for predicting the mold fill times and resin flow path during composite manufacturing. In this work, we report an efficient approach to predict the permeability of 3D microstructures from deep learning based permeability predictions of 2D cross-sections combined via a circuit analogy. After validating the network’s predictions in 2D and extending it to 3D, we investigate its capabilities for handling images of various sizes obtained from virtual and real microstructures. More than 90% of 2D predictions is within ± 30% of their counterparts obtained via flow simulations, similarly for 3D transverse permeability predictions, while in 3D case computational time is reduced from several thousands of seconds to less than 10 s. This work provides a robust and efficient framework for characterizing the permeability of fibrous microstructures and paves the way for extending this capability to estimate the permeability of fabric mesostructures.