This paper is devoted to the inviscid limit of the generalized complex Ginzburg-Landau (CGL) equation: \[ \begin{cases}\partial_t u=(a+i\nu)\Delta_x u+Ru-(b+i\mu)f(u)\;\text{in} \Omega,\;t>0\\ U(x,0)=u_0(x),\quad x\in\Omega.\end{cases}\tag{1} \] The authors consider (1) in the whole space \(\Omega=\mathbb{R}^d\) as well as in the torus \(T^d=(\mathbb{R}/2\pi\mathbb{Z})\). The parameters \(a, b, \nu, \mu, R\) are real with \(R\geq 0\), \(a>0\), and \(b>0\). The interaction term is \(f(u)=u\cdot|u|^{2\sigma}\), \(u\in\mathbb{C}\), for some \(\sigma>0\). The authors show that in the inviscid limit the CGL equation reduces to the nonlinear Schrödinger equation. This limit is proved rigorously with \(H^1\) data in the whole space \(\mathbb{R}^d\) for the Cauchy problem and in the torus with periodic boundary conditions. The basic idea is to treat the CGL equation as a perturbation of the nonlinear Schrödinger equation. Moreover, optimal convergence rates are proved.