The linear and the third‐order nonlinear optical absorption spectra of a donor impurity confined by a quantum ring are studied using the matrix diagonalization method within the effective‐mass approximation. The linear and the third‐order nonlinear optical absorption coefficients between the ground (L = 0) and the first excited state (L = 1) have been examined based on the computed energies and wavefunctions. The results are presented as a function of the incident photon energy for the different values of the confinement strength, the incident optical density and the ring radius. We found the confinement strength, the incident optical density and the ring radius have a great effect on the linear, the third‐order nonlinear and total absorption spectra. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)