Denoising generative models have recently become the dominant paradigm for dexterous grasp generation, owing to their ability to model complex grasp distributions from large-scale data. However, existing diffusion-based methods typically formulate generation as a stochastic differential equation (SDE), which often requires many sequential denoising steps and introduces trajectory instability that can lead to physically infeasible grasps. In this paper, we propose EFF-Grasp, a novel Flow-Matching-based framework for physics-aware dexterous grasp generation. Specifically, we reformulate grasp synthesis as a deterministic ordinary differential equation (ODE) process, which enables efficient and stable generation through smooth probability flows. To further enforce physical feasibility, we introduce a training-free physics-aware energy guidance strategy. Our method defines an energy-guided target distribution using adapted explicit physical energy functions that capture key grasp constraints, and estimates the corresponding guidance term via a local Monte Carlo approximation during inference. In this way, EFF-Grasp dynamically steers the generation trajectory toward physically feasible regions without requiring additional physics-based training or simulation feedback. Extensive experiments on five benchmark datasets show that EFF-Grasp achieves superior performance in grasp quality and physical feasibility, while requiring substantially fewer sampling steps than diffusion-based baselines.