A theory, which includes many‐body effects, is presented for the interband absorption in a pseudomorphic Ga1−yAlyAs/InxGa1−xAs/GaAs modulation‐doped quantum well. The electron‐electron interaction in a degenerate Fermi sea is calculated in the self‐consistent Hartree approximation. In addition, the binding energy within an electron‐hole pair is included in the ladder approximation as a vertex correction to the response function. Due to the subband structure arising from the quantization by the quantum well, there are different types of excitons associated with the electrons and holes in different subbands. In the theory, the coupling between excitons is calculated in the random‐phase approximation. The numerical results for the temperature dependence of the absorption peaks at the Fermi edge (low temperature) and the band edge (room temperature) compare well with available experimental data which was obtained in electric‐field modulated photoreflectance experiments. At low temperatures, the theory shows that there are important modifications to the single‐particle model. The Fermi energy is extracted by fitting the calculated results to the thermally broadened line shape of the absorption spectrum. As a consequence, the electron density of the quantum wells can be accurately determined by means of this contactless, nondestructive, rapid and simple characterization method. Moreover, information on the alloy composition, built‐in electric field, and the interface stress can also be obtained.