In this research work, a resilient finite-time consensus-based distributed secondary control protocol is presented for droop-based distributed generating (DG) units of an islanded AC microgrid (MG). Through a multi-agent control structure, the DG units of the microgrid adjust their active power outputs so that they reach an agreed-upon value in a finite time. Concurrently, all the DG units are forced to operate with their frequencies regulated to the reference MG frequency in a finite time, despite time-varying load perturbations. Each DG unit is provided with a hierarchical control architecture, where the primary control is achieved using the droop control method, while the secondary control is established through the proposed distributed control protocol. The communication between DG units takes place over a sparse communication network. The proposed control protocol is robust to both small and sufficiently large communication latencies and it supports the plug-and-play feature of DG units. Different time-domain-based numerical simulations are carried out on a small as well as large microgrid testbenches in Matlab/Simulink and demonstrate the correctness and effectiveness of the proposed distributed control protocol. A comparative study is also presented with the existing distributed control protocol, and it is found that the proposed strategy is superior in its performance.