A filter housing has a first housing part with a first rim section and a second housing part with a second rim section. The housing parts can be joined and separated from each other in axial mounting direction and define a housing interior for a filter element provided with a circumferentially extending sealing element. The first and second rim sections form a receiving area in which the sealing element is seal-tightly clamped radially between the first and second rim sections when the housing parts are joined in the mounted state. A snap connecting device axially braces the first and second housing parts relative to each other. The snap connecting device is formed integrally on the first and second housing parts such that a clamping force applied by the first and second rim sections on the sealing element in radial direction is decoupled from the snap connecting device.