<p>This study aims to investigate the singularly perturbed generalized Hodgkin–Huxley equation that serves to model and examine rapid neuronal action potential transitions under varying circumstances. It entails to determine analytical solutions of the governing equation by utilizing Lie approximate symmetry analysis. We procure a six-dimensional Lie algebra, which, in accordance with the Olver’s Optimal theory results in the construction of optimal system, thereby transforming the partial differential equation into a set of ordinary differential equations. Further, the tanh–coth method is utilized to derive the group invariant analytical solutions for certain symmetry reductions. Approximate solutions are presented alongside their associated error analyses, including tables and residual plots. The graphical representations for certain exact solutions are provided after assigning appropriate parameter values to enhance the visual understanding of the results.</p>