Nuclear magnetic resonance flow imaging (MRFI) was used to measure fluid flow noninvasively in the extracapillary space (ECS) of a hollow‐fiber bioreactor without cells. Agreement between these axial flow measurements in a single hollow‐fiber module and predicted axial velocity contour plots at various image planes along the path length was good. Flow in a solid‐wall tube (phantom) was first used to calibrate pixel intensities with axial velocities. Flow images at several locations along the permeable hollow fiber length were then obtained in order to observe the well‐known leakage or Starling flow in the ECS. These quantitative spatially dependent velocity measurements were then compared to theoretically derived velocities obtained from a solution of Poisson's equation with a constant pressure gradient and no slip at the solid surfaces. A mathematical transformation was used to simplify the numerical methods. Leakage flow through the ECS of a multifiber bioreactor (40 fibers) was also measured by MRFI, illustrating the applicability of this method for optimizing operational procedures and design of membrane bioreactors and filtration devices.