The San Andreas Fault Observatory at Depth (SAFOD) scientific borehole near Parkfield, California crosses two actively creeping shear zones at a depth of 2.7 km. Core samples retrieved from these active strands consist of a foliated, Mg-clay-rich gouge containing porphyroclasts of serpentinite and sedimentary rock. The adjacent damage zone and country rocks are comprised of variably deformed, fine-grained sandstones, siltstones, and mudstones. We conducted laboratory tests to measure the permeability of representative samples from each structural unit at effective confining pressures, Pe up to the maximum estimated in situ Pe of 120 MPa. Permeability values of intact samples adjacent to the creeping strands ranged from 10−18 to 10−21 m2 at Pe = 10 MPa and decreased with applied confining pressure to 10−20–10−22 m2 at 120 MPa. Values for intact foliated gouge samples (10−21–6 × 10−23 m2 over the same pressure range) were distinctly lower than those for the surrounding rocks due to their fine-grained, clay-rich character. Permeability of both intact and crushed-and-sieved foliated gouge measured during shearing at Pe ≥ 70 MPa ranged from 2 to 4 × 10−22 m2 in the direction perpendicular to shearing and was largely insensitive to shear displacement out to a maximum displacement of 10 mm. The weak, actively-deforming foliated gouge zones have ultra-low permeability, making the active strands of the San Andreas Fault effective barriers to cross-fault fluid flow. The low matrix permeability of the San Andreas Fault creeping zones and adjacent rock combined with observations of abundant fractures in the core over a range of scales suggests that fluid flow outside of the actively-deforming gouge zones is probably fracture dominated.