This article presents a rigorous error estimation of the method of auxiliary sources (MAS) when applied to the solution of the electromagnetic scattering problem involving dielectric objects. The geometry investigated herein is a circular, dielectric cylinder of infinite length. The MAS matrix is inverted analytically, via advanced eigenvalue analysis, and an exact expression for the boundary condition error owing to discretization is derived. Furthermore, an analytical formula for the condition number of the linear system is also extracted, explaining the irregular behavior of the computational error resulting from numerical matrix inversion. Also, the effects of the dielectric parameters on the error are fully investigated. Finally, the optimal location of the auxiliary sources is determined on the grounds of error minimization.