In this paper, we propose a proximal physics-informed normalized least-mean-squares (Prox-PI-NLMS) algorithm for acoustic echo cancellation (AEC). The method integrates physically motivated priors on the acoustic impulse response within an adaptive filtering framework by combining stochastic gradient updates with proximal operators. In particular, exponential decay, sparsity, temporal smoothness, spectral smoothness, and slow temporal variation are jointly enforced through a composite regularization strategy, where non-smooth penalties are handled via efficient proximal mappings. This formulation enables the incorporation of structured prior knowledge without compromising the low-complexity nature of NLMS. Numerical results under colored excitation demonstrate that the proposed Prox-PI-NLMS achieves improved convergence behavior and reduced steady-state error compared to conventional and sparsity-aware adaptive filtering algorithms, while maintaining a reduced computational complexity.