New seismic imaging and seismotectonic data from the southwest Iberian margin, the site of the present-day boundary between the European and African plates, reveal that active strike slip is occurring along two prominent lineaments that have recently been mapped using multibeam bathymetry. Multichannel seismic and subbottom profiler images acquired across the lineaments show seafloor displacements and active faulting to depths of at least 10 km and of a minimum length of 150 km. Seismic moment tensors show predominantly WNW–ESE right-lateral strike-slip motion, i.e., oblique to the direction of plate convergence. Estimates of earthquake source depths close to the fault planes indicate upper mantle (i.e., depths of 40–60 km) seismogenesis, implying the presence of old, thick, and brittle lithosphere. The estimated fault seismic parameters indicate that the faults are capable of generating great magnitude (Mw ≥ 8.0) earthquakes. Such large events raise the concomitant possibility of slope failures that have the potential to trigger tsunamis. Consequently, our findings identify an unreported earthquake and tsunami hazard for the Iberian and north African coastal areas.