An adsorber element for a filter system is provided with a frame that has a base plate and one or more rigid support elements that project away from the base plate. An adsorber medium is disposed at the frame and arranged at least in sections of the base plate and at least in sections of the one or more rigid support elements. The filter system has a housing with an inlet and an outlet. The filter system is flowed through by a gaseous fluid from the inlet to the outlet. A filter element is arranged in the housing between inlet and outlet. The adsorber element is arranged in the housing preferably downstream of the filter element.