Convective flow in the mantle and the motions of tectonic plates produce deformation of Earth's interior, and the rock fabric produced by this deformation can be discerned using the anisotropy of the seismic wave speed. This deformation is commonly inferred close to lithospheric boundaries beneath the ocean in the uppermost mantle, including near seafloor-spreading centres as new plates are formed via corner flow, and within a weak asthenosphere that lubricates large-scale plate-driven flow and accommodates smaller scale convection. Seismic models of oceanic upper mantle differ as to the relative importance of these deformation processes: seafloor spreading fabric is very strong just beneath the crust-mantle boundary (the Mohorovičić discontinuity, or Moho) at relatively local scales, but at the global and ocean-basin scales, oceanic lithosphere typically appears weakly anisotropic when compared to the asthenosphere. Here we use Rayleigh waves, recorded across an ocean-bottom seismograph array in the central Pacific Ocean (the NoMelt Experiment), to provide unique localized constraints on seismic anisotropy within the oceanic lithosphere-asthenosphere system in the middle of a plate. We find that azimuthal anisotropy is strongest within the high-seismic-velocity lid, with the fast direction coincident with seafloor spreading. A minimum in the magnitude of azimuthal anisotropy occurs within the middle of the seismic low-velocity zone, and then increases with depth below the weakest portion of the asthenosphere. At no depth does the fast direction correlate with the apparent plate motion. Our results suggest that the highest strain deformation in the shallow oceanic mantle occurs during corner flow at the ridge axis, and via pressure-driven or buoyancy-driven flow within the asthenosphere. Shear associated with motion of the plate over the underlying asthenosphere, if present, is weak compared to these other processes.