A self-powered skin patch for the measurement of sweat conductivity is presented. The key component of the patch consists of a paper battery that is activated upon absorption of sweat. This body fluid acts as the battery electrolyte, the conductivity of which has a direct impact on the battery-generated output power and voltage. This particular behaviour enables the operation of a very simple and robust conductivity sensor in direct current mode without needing an external power source. The device presented in this paper takes advantage of this new measurement method to develop a sweat patch for screening cystic fibrosis that operates with an extremely simple electronic circuit that minimizes its cost and environmental impact. The patch provides an unambiguous digital result that can be read in an electrochromic display and yields 95% sensitivity and 100% specificity when tested with artificial eccrine perspiration samples.