Fluid flow through intricate confining geometries often exhibits complex behaviors, certainly in porous materials, e.g., in groundwater flows or the operation of filtration devices and porous catalysts. However, it has remained extremely challenging to measure 3D flow fields in such micrometer-scale geometries. Here, we introduce a new 3D velocimetry approach for optically opaque porous materials, based on time-resolved x-ray micro-computed tomography (CT). We imaged the movement of x-ray tracing micro-particles in creeping flows through the pores of a sandpack and a porous filter, using laboratory-based CT at frame rates of tens of seconds and voxel sizes of 12 μm. For both experiments, fully three-dimensional velocity fields were determined based on thousands of individual particle trajectories, showing a good match to computational fluid dynamics simulations. Error analysis was performed by investigating a realistic simulation of the experiments. The method has the potential to measure complex, unsteady 3D flows in porous media and other intricate microscopic geometries. This could cause a breakthrough in the study of fluid dynamics in a range of scientific and industrial application fields.