A membrane humidifier has multiple stacking units mounted one on top of the other, where an individual stacking unit includes a flow plate and diffusion unit, where a circumference of the diffusion unit is formed by two oppositely situated first edge sides and two oppositely situated second edge sides. The diffusion unit includes: a top layer on a top side of the diffusion unit, a bottom layer on a bottom side of the diffusion unit, a moisture-permeable membrane, two oppositely situated upper receiving elements at the two first edge sides, on the top side of the diffusion unit, and two oppositely situated lower receiving elements at the two second edge sides, on the bottom side of the diffusion unit, where the flow plate of the stacking unit is inserted into the two lower receiving elements, and where the next stacking unit is inserted into the two upper receiving elements.