In this study, linear, nonlinear and total optical absorption coefficients related a single shallow donor atom confined in semiconductor core/shell/shell quantum dot heterostructure are researched in detail within the compact density matrix formalism approximation. For this purpose, firstly, the energies and the wavefunctions are computed by the diagonalization method in the effective mass approach. Moreover, the effects of size modulation, donor position and magnetic field are analyzed. The numerical results indicate that the linear and nonlinear parts of the absorption coefficients related with intersubband 1s-1p and 1p-1d donor transitions undergo significant changes.