Melting of solids is a fundamental natural phenomenon whose pressure dependence has been of interest for nearly a century. However, the temporal evolution of the molten phase under pressure has eluded measurements because of experimental challenges. By using the shock front as a fiducial, we investigated the time-dependent growth of the molten phase in shock-compressed germanium. In situ x-ray diffraction measurements at different times (1 to 6nanoseconds) behind the shock front quantified the real-time growth of the liquid phase at several peak stresses. These results show that the characteristic time for melting in shock-compressed germanium decreases from ~7.2nanoseconds at 35gigapascals to less than 1nanosecond at 42gigapascals. Our melting kinetics results suggest the need to consider heterogeneous nucleation as a mechanism for shock-induced melting and provide an approach to measuring melting kinetics in shock-compressed solids.