We report pulsed terahertz (THz) emission from solution-processed metal halide perovskite films with electric field 1 order of magnitude lower than p-InAs, an efficient THz emitter. Such emission is enabled by a unique combination of efficient charge separation, high carrier mobilities, and more importantly surface defects. The mechanism of generation was identified by investigating the dependence of the THz electric field amplitude on surface defect densities, excess charge carriers, excitation intensity and energy, temperature, and external electric field. We also show for the first time THz emission from a curved surface, which is not possible for any crystalline semiconductor and paves the way to focus high-intensity sources. These results represent a possible new direction for perovskite optoelectronics and for THz emission spectroscopy as a complementary tool in investigating surface defects on metal halide perovskites, of fundamental importance in the optimization of solar cells and light-emitting diodes.