By means of THz pump and optical probe spectroscopy, we observed that the incident THz pulse induces a strong spectral modulation of the 1s heavy-hole exciton peak of GaAs quantum wells due to Rabi splitting. Our precise measurements in the time domain show that the Rabi splitting follows the instantaneous THz electric pulse at extremely strong fields but persists up to a negative delay time of similar to 1 ps at weak fields. This field dependent dynamics of the Rabi splitting indicates that the excitonic field ionization governs a nonperturbative nonlinear dynamics of excitons by causing a reduction of the dephasing time.