An integral equation is formulated to describe electromagnetic wave transmission through a subwavelength nano-hole in a thin plasmonic sheet in terms of the dyadic Green's function for the associated Helmholtz problem. Taking the subwavelength radius of the nano-hole to be the smallest length of the system, we have obtained an exact solution of the integral equation for the dyadic Green's function analytically and in closed form. This dyadic Green's function is then employed in the numerical analysis of electromagnetic wave transmission through the nano-hole for normal incidence of the incoming wave train. The electromagnetic transmission involves two distinct contributions; one emanates from the nano-hole, and the other is directly transmitted through the thin plasmonic layer itself (which would not occur in the case of a perfect metal screen). The transmitted radiation exhibits interference fringes in the vicinity of the nano-hole, and they tend to flatten as a function of increasing lateral separation from the hole, reaching the uniform value of transmission through the sheet alone at large separations.