Tsunami generation from earthquake-induced seafloor deformations has long been recognized as a major hazard to coastal areas. Strike-slip faulting has generally been considered insufficient for triggering large tsunamis, except through the generation of submarine landslides. Herein, we demonstrate that ground motions due to strike-slip earthquakes can contribute to the generation of large tsunamis (>1 m), under rather generic conditions. To this end, we developed a computational framework that integrates models for earthquake rupture dynamics with models of tsunami generation and propagation. The three-dimensional time-dependent vertical and horizontal ground motions from spontaneous dynamic rupture models are used to drive boundary motions in the tsunami model. Our results suggest that supershear ruptures propagating along strike-slip faults, traversing narrow and shallow bays, are prime candidates for tsunami generation. We show that dynamic focusing and the large horizontal displacements, characteristic of strike-slip earthquakes on long faults, are critical drivers for the tsunami hazard. These findings point to intrinsic mechanisms for sizable tsunami generation by strike-slip faulting, which do not require complex seismic sources, landslides, or complicated bathymetry. Furthermore, our model identifies three distinct phases in the tsunamic motion, an instantaneous dynamic phase, a lagging coseismic phase, and a postseismic phase, each of which may affect coastal areas differently. We conclude that near-source tsunami hazards and risk from strike-slip faulting need to be re-evaluated.