Shear-wave anisotropy in Earth's mantle helps constrain the lattice-preferred orientation of anisotropic minerals due to viscous flow. Previous studies at the Japan Trench subduction zone using land-based seismic networks identified strong anisotropy in the mantle wedge, reflecting viscous flow induced by the subducting slab. Here we map anisotropy in the previously uninvestigated offshore region by analyzing shear waves from interplate earthquakes that are recorded by a new seafloor network (the S-net). The newly detected anisotropy is not in the mantle wedge but only in the overlying crust (∼0.1 s time delay and trench-parallel fast direction). The distinct lack of anisotropy indicates that the forearc mantle wedge offshore is decoupled from the slab and does not participate in the viscous flow, in sharp contrast with the rest of the mantle wedge. A stagnant forearc mantle wedge provides a stable and cold tectonic environment that is important for the petrological evolution and earthquake processes of subduction zones.