We study luminescence spectra observed from InAs quantum dots (QDs) embedded in an n-type InGaAs-based heterostructure, where electron Cooper pairs penetrate from an adjacent niobium (Nb) superconductor with the proximity effect. Below the superconducting (SC) critical temperature of Nb, we observe substantial luminescence intensity enhancement and a sharp edge in luminescence spectra of InAs QDs. We explain the observed sharp edge in the luminescence spectra with the proximity effect, that is, with the consideration of opening of SC gap and modification of density of states (DOS) near the electron Fermi level in the n-type semiconductor heterostructure. We demonstrate that the sharp edge luminescence spectra are well reproduced by the SC DOS, with quasiparticle lifetime broadening and a Gaussian distribution of lowest QD state emission lines. We discuss the reason why it has been difficult to observe the sharp edge luminescence spectra in the previous quantum well-based SC light emitting diodes.