The rapid proliferation of distributed renewable generation within microgrids introduces critical stability challenges, including voltage fluctuations, frequency deviations, and power quality degradation, particularly at high penetration levels exceeding 70%. Conventional optimization approaches for microgrid control parameter tuning either rely on steady-state Optimal Power Flow (OPF) solvers that neglect transient dynamics, or employ metaheuristic algorithms that treat physics constraints as soft penalties, frequently producing electrically infeasible solutions. This paper presents Physics-Informed MEtaheuristic for Microgrid Stability (PI-MEMS), a novel framework that integrates fundamental power system physics directly into a hybrid Differential Evolution–Grey Wolf Optimizer (DE-GWO) metaheuristic. The key innovation is a Physics-Informed Fitness Evaluation (PIFE) that embeds Kirchhoff's laws, AC power flow equations, voltage/frequency droop control constraints, and inverter dynamics into the optimization loop, guaranteeing that every candidate solution satisfies electrical engineering constraints without post-hoc repair. Additional contributions include: 1) a Physics-Informed Neural Network (PINN) transient stability surrogate trained on swing equation dynamics for rapid stability margin assessment, 2) multi-timescale optimization addressing steady-state OPF and dynamic transient stability simultaneously, 3) stochastic scenario generation for renewable uncertainty using Gaussian copula models, and 4) an adaptive hybrid mechanism switching between Differential Evolution (DE) exploitation and Grey Wolf Optimizer (GWO) exploration based on constraint violation patterns. PI-MEMS is evaluated on Institute of Electrical and Electronics Engineers (IEEE) 33-bus and IEEE 69-bus modified distribution test systems with embedded microgrids, a Malaysian rural microgrid in Sarawak (Borneo), and an Egyptian industrial microgrid at the New Administrative Capital (NAC). Results demonstrate voltage deviation reductions of 38–52%, frequency stability improvements of 22–35% (measured by rate of change of frequency (RoCoF) and nadir metrics), and 15–24% reductions in total energy cost compared to standard DE, GWO, Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and conventional OPF solvers. Critically, all PI-MEMS solutions are physics-feasible with zero constraint violations, compared to 3–12% violation rates in baseline metaheuristics.