Measuring water self-diffusion in the oriented structure of stretched Nafion represents an effective way of studying the correlations between the stress-induced order and the transport properties of the membrane. In this work, we performed pulsed-field gradient NMR experiments to investigate water self-diffusion in a single membrane under traction. The data were collected with a high signal-to-noise ratio and small draw ratio steps using a specially design NMR probe together with a mini traction apparatus. The results demonstrate that the anisotropy of diffusion is much larger in a membrane under traction than in a stack of membranes that were uniaxiafly stretched at high temperature before the measurements. Arguments based on the mechanical properties of Nafion can explain qualitatively the observed differences by highlighting the important role of both applied stress and temperature in the stress-induced order. We used a simple, but realistic, deformation model to analyze the experimental data by extracting the evolution of the diffusion anisotropy as a function of the orientational order parameter of the water conducting channels. Finally, we made analogies between the self-diffusion of water in the anisotropic structure of stretched Nafion and the Brownian dynamics of elongated particles.