We report the first terahertz study of the intraexcitonic 1s-2p transition at high excitation densities in GaAs∕AlxGa1−xAs quantum wells. A strong shift, broadening, and ultimately the disappearance of this resonance occurs with increasing density, after ultrafast photoexcitation at the near-infrared exciton line. Densities of excitons and unbound electron-hole pairs are followed quantitatively using a model of the composite terahertz dielectric response. Comparison with near-infrared absorption changes reveals a significantly enhanced energy shift and broadening of the intraexcitonic resonance.