We investigate the aftershock sequence of the 2014 Mw 6.0 South Napa, California, earthquake. Low‐magnitude aftershocks missing from the network catalog are detected by applying a matched‐filter approach to continuous seismic data, with the catalog earthquakes serving as the waveform templates. We measure precise differential arrival times between events, which we use for double‐difference event relocation in a 3D seismic velocity model. Most aftershocks are deeper than the mainshock slip, and most occur on the west of the mapped surface rupture. Although the mainshock coseismic and postseismic slip appears to have occurred on the near‐vertical, strike‐slip West Napa fault, many of the aftershocks occur in a complex zone of secondary faulting. Earthquake locations in the main aftershock zone, near the mainshock hypocenter, delineate multiple dipping secondary faults. Composite focal mechanisms indicate strike‐slip and oblique‐reverse faulting on the secondary features. The secondary faults were moved toward failure by Coulomb stress changes from the mainshock slip. Clusters of aftershocks north and south of the main aftershock zone exhibit vertical strike‐slip faulting more consistent with the West Napa fault. The northern aftershocks correspond to the area of the largest mainshock coseismic slip, whereas the main aftershock zone is adjacent to the fault area that has primarily slipped postseismically. Unlike most creeping faults, the zone of postseismic slip does not appear to contain embedded stick‐slip patches that would have produced on‐fault aftershocks. The lack of stick‐slip patches along this portion of the fault may contribute to the low productivity of the South Napa aftershock sequence.