We investigate polarization-dependent ultrafast photocurrents in the Weyl semimetal TaAs using terahertz (THz) emission spectroscopy. Our results reveal that highly directional, transient photocurrents are generated along the noncentrosymmetric c axis regardless of incident light polarization, while helicitydependent photocurrents are excited within the ab plane. This is consistent with earlier static photocurrent experiments, and demonstrates on the basis of both the physical constraints imposed by symmetry and the temporal dynamics intrinsic to current generation and decay that optically induced photocurrents in TaAs are inherent to the underlying crystal symmetry of the transition metal monopnictide family of Weyl semimetals.