We investigate the electronic structure of a specially prepared highly dense conventional high temperature superconductor, MgB2, employing high resolution photoemission spectroscopy. The spectral evolution close to the Fermi energy is commensurate to BCS descriptions as expected. However, the spectra in the wider energy range reveal the emergence of a pseudogap much above the superconducting transition temperature indicating an apparent departure from the BCS scenario. The energy scale of the pseudogap is comparable to the energy of the E2g phonon mode responsible for superconductivity in MgB2 and the pseudogap can be attributed to the effect of electron-phonon coupling on the electronic structure. These results reveal a scenario of the emergence of the superconducting gap within an electron-phonon coupling induced pseudogap and have significant implications in the study of high temperature superconductors.