Designing protection for a DC microgrid is challenging due to its DC nature and heavily capacitor-dominated DC bus that induces high amplitude current spike during short-circuit faults. Moreover, for small-scale applications such as residential DC microgrids, low line-resistance cables increase the fault detection time constraint. Thus, this paper proposes a fast short-circuit fault detection and isolation method based on current residual computation for a standalone residential DC microgrid. The proposed method continuously compares the computed residual from sensed branch currents to their respective defined thresholds. These thresholds are predetermined by analyzing the microgrid operation in healthy mode, considering both steady-state and transient operations. The protection device isolating the faulty branch is then activated once the corresponding residual exceeds its threshold. The protection scheme is validated through a processor-in-the-Loop simulation approach, during which the power stage of the system remains simulated on the host computer using PSIM software, while its control algorithm is executed from a Texas Instrument TMS320F28335 hardware target. The proposed protection algorithm is able to discriminate transient perturbations due to load connection from short-circuit faults. Furthermore, the algorithm implementation is not limited by the size of the DC microgrid nor by the type of the connected loads.