A semiconductor sensor device includes a sensor chip. The sensor chip includes a sensor region and contact areas on its upper side and is further arranged in a cavity housing. The cavity housing includes side walls, a housing bottom, a cavity, external contacts on the outside of the cavity and contact pads on an upper side of the housing bottom facing the cavity. The sensor chip is embedded into a rubber-elastic plastic composition within the cavity of the cavity housing such that the sensor region of the sensor chip faces the housing bottom and the contact areas of the sensor chip are electrically connected to the contact pads on the housing bottom via elastic flip-chip contacts.