The increasing penetration of distributed generators (DGs) in modern day power grids results in varying fault current levels and network scenarios which may affect the conventional overcurrent protection relays. This necessitates a protection scheme with efficient fault signal estimations and smart decision-making capabilities in case of unexpected events. In this paper, a novel, fast, and adaptive relay mechanism has been proposed for complete protection of radial distribution systems with DG penetration. A fast recursive discrete Fourier transform (FRDFT) algorithm is used here for efficient fundamental tracking of varying power system signals. The numerical relay design using the FRDFT algorithm is embedded with a fuzzy-logic decision-making module for obtaining optimal protection settings in case of changing system conditions. The proposed adaptive scheme is tested on a standard IEEE 34-bus distribution system equipped with DGs by simulating various case studies. Simulation results verify that the adaptive relay is able to capture the changing system scenarios and select the protection settings accordingly.