We examine possible sources of a small tsunami produced by the 1906 San Francisco earthquake, recorded at a single tide gauge station situated at the opening to San Francisco Bay. Coseismic vertical displacement fields were calculated using elastic dislocation theory for geodetically constrained horizontal slip along a variety of offshore fault geometries. Propagation of the ensuing tsunami was calculated using a shallow-water hydrodynamic model that takes into account the effects of bottom friction. The observed amplitude and negative pulse of the first arrival are shown to be inconsistent with small vertical displacements (~4-6 cm) arising from pure horizontal slip along a continuous right bend in the San Andreas fault offshore. The primary source region of the tsunami was most likely a recently recognized 3 km right step in the San Andreas fault that is also the probable epicentral region for the 1906 earthquake. Tsunami models that include the 3 km right step with pure horizontal slip match the arrival time of the tsunami, but underestimate the amplitude of the negative first-arrival pulse. Both the amplitude and time of the first arrival are adequately matched by using a rupture geometry similar to that defined for the 1995 MW (moment magnitude) 6.9 Kobe earthquake: i.e., fault segments dipping toward each other within the stepover region (83??dip, intersecting at 10 km depth) and a small component of slip in the dip direction (rake=-172??). Analysis of the tsunami provides confirming evidence that the 1906 San Francisco earthquake initiated at a right step in a right-lateral fault and propagated bilaterally, suggesting a rupture initiation mechanism similar to that for the 1995 Kobe earthquake.