The electronic structure and morphology of ultrathin MgO films epitaxially grown on Ag(001) were investigated using low-temperature scanning tunneling spectroscopy and scanning tunneling microscopy. Layer-resolved differential conductance (dI/dU) measurements reveal that, even at a film thickness of three monolayers, a band gap of about 6 eV is formed corresponding to that of the MgO(001) single-crystal surface. This finding is confirmed by layer-resolved calculations of the local density of states based on density functional theory.