We report pump-probe measurements of a hydrogen molecule (H_{2}) in the tunnel junction of a scanning tunneling microscope coupled to ultrashort terahertz (THz) pulses. The coherent oscillation of the THz-induced dc tunneling current at a frequency of ∼0.5 THz fingerprints the absorption by H_{2} as a two-level system (TLS). Two components of the oscillatory signal are observed and point to both photon and field aspects of the THz pulses. A few loosely bound states with similar energies for the upper state of the TLS are evidenced by the coherent revival of oscillatory signal. Furthermore, the comparison of spectroscopic features of H_{2} with different tips provides an understanding of the TLS for H_{2}.