We have investigated the effects of the built-in electric field in ${\mathrm{G}\mathrm{a}\mathrm{N}/\mathrm{A}\mathrm{l}}_{0.15}{\mathrm{Ga}}_{0.85}\mathrm{N}$ quantum wells by photoluminescence spectroscopy. The fundamental electron heavy-hole transition redshifts well below the GaN bulk gap for well widths larger than 3 nm for the specific quantum wells investigated and exhibits a concomitant reduction of the intensity with increasing well thickness. The experimental data are quantitatively explained by means of a self-consistent tight-binding model that includes screening (either dielectric or by free-carriers), piezoelectric field and spontaneous polarization field. The impact of the built-in field on the exciton stability is discussed in detail. We demonstrate that the exciton binding energy is substantially reduced by the built-in field, well below the values expected from the quantum size effect in the flat band condition.