An encapsulation device for operating a sensor in an explosive atmosphere includes a receiving space designed to receive the sensor and a protective housing having at least one gas-permeable wall portion that permits gas exchange between an interior space of the encapsulation device and an environment of the encapsulation device through the gas-permeable wall portion. A quenching volume is arranged to extend along an inner side of the protective housing and is filled with a filling material. The quenching volume at least partially surrounds the receiving space. A gas-permeable filter element is disposed between the quenching volume and the receiving space, and bounds the quenching volume with respect to the receiving space.