This article proposes the closed-form solution of the generalized non-Fourier model-based bioheat transfer equation (BHTE) in Cylindrical coordinates to understand the thermal behavior of living tissue heated by a pulsed laser. The axisymmetric living tissue exposed to the non-Gaussian temporal profile of laser heating has been considered to investigate the non-Fourier bioheat transfer phenomena. The closed-form solution of the generalized non-Fourier model-based BHTE with time-dependent thermal energy generation has been obtained through the finite integral transform (FIT) technique. The analytical solution was juxtaposed to the corresponding numerical solution in order to determine its reliability. The numerical solution of the aforementioned governing equation has been obtained by the finite volume method (FVM). The results of both analytical and numerical solutions have been verified using results given in published literature. Subsequently, the dual-phase-lag (DPL) model's findings were juxtaposed to those obtained using the hyperbolic and traditional Fourier models. The effect of different parameters like relaxation times corresponding to the temperature gradient and heat flux, metabolic energy generation, and blood perfusion on the resultant temperature distribution inside the axisymmetric living tissue exposed to pulsed laser heating has been discussed. The importance of this study might be found in various applications such as laser-based-photothermal therapy, melting of the surface of metal and alloys by laser heating.