We present an efficient approach for the solution of the 2-D forward electromagnetic scattering problem related to arbitrary-shaped multilayer cylinders having embedded inhomogeneities. For this purpose, we combine the method of moments (MoM) with the previously introduced approach that enables simple and fast computation of the field scattered from arbitrary-shaped multilayer cylinders through the expansion of the field into a series of cylindrical functions. The MoM is applied for the computation of the field scattered from the embedded inhomogeneity only by discretizing it. In order to apply MoM in such a manner, first, the above-mentioned series representation approach is applied straightforwardly for the computation of the field scattered from the multilayer background. Then, we propose an adaptation of this approach for fast computation of the integral of the background Green's function over each cell of the MoM mesh. This adaptation also deals with the singularity of the Green's function. The efficiency of the method is shown in various numerical simulations.