We have recorded piezoreflectance (PzR) spectra at 15 K over the energy range 1.5 - 2.5 eV for undoped, 0.5% and 1% rhenium-doped (Re-doped) MoS₂ single crystals to examine the effect of dopant on the spectral features near the direct band- edge excitonic transitions. More elaborate temperature dependences of the excitonic features A and B of the Re-doped MoS₂ single crystals in the range 15 to 300 K have also been obtained using PzR. The energies and broadening parameters of the A and B excitons of the Re-doped MoS₂ samples have been determined accurately via a detailed line shape fit of the PzR spectra. The parameters that describe the temperature variation of the energies and broadening functions of the excitonic transitions are analysed. A plausible suggestion will be put forth to explain the role of rhenium in affecting the variation of the excitonic transitions.