The discontinuous character of the exact-exchange-correlation (xc) energy functional of density functional theory is shown to arise naturally in the subband spectra of semiconductor quantum wells. Using an ab initio xc functional, including exchange exactly and correlation in an exact partial way, a discontinuity appears in the xc potential, each time a subband becomes slightly occupied. Exchange and correlation give opposite contributions to the discontinuity, with correlation overcoming exchange. The jump in the intersubband energy is in excellent agreement with experimental data.