A moisture exchange module has a bundle of moisture-permeable hollow fiber membranes and at least one line element for supplying a gas stream that flows through the hollow fibers in an inner flow. The at least one line element opens out into an inflow region, which is of at least approximately the same cross section as the bundle of hollow fiber membranes. According to the present invention, the at least one line element opens out into the inflow region at an angle of from 60° to 120° with respect to the longitudinal axis of the bundle of hollow fiber membranes without the longitudinal axes of the one line element and of the bundle of hollow fiber membranes intersecting one another. An annular diverter means for diverting the gas flow are provided between the cross section of the line elements through which gas can flow and the inflow region. The diverter means are arranged in such a way that an annular gap is formed, which annular gap is connected to the at least one line element and, on its side remote from the bundle of hollow fiber membranes, is connected to the inflow region.