A moisture exchange module includes a bundle of moisture-permeable hollow fiber membranes. It is provided with a feedline for supplying a gas stream that flows through the hollow fiber membranes in an inner flow. According to the present invention, a separating device for separating out liquid particles from the gas flow are provided in the region between the feedline and the bundle of hollow fiber membranes. The separating device may have the form of a groove and are arranged in such a way that the gas flow is guided in such a manner that the centrifugal force assists movement of the liquid particles towards the separating device. The moisture exchange module preferably forms part of a fuel cell system to humidify feed air for the fuel cell system.