Crust produced at mid-ocean ridges with full spreading rates less than ∼20 mm/yr is observed to be only 0–4 km thick, well below the global average of 6–7 km for oceanic crust produced at faster spreading rates. The origin of this difference is unknown, but is speculated to result from a thicker thermal boundary layer at the axis of the slowest spreading ridges that either inhibits shallow melting or melt extraction. We present an analysis of regional broadband data, predominately Love and Rayleigh waves, collected along the very slow spreading Mohns Ridge (where crustal thickness is ∼4 km) in the Norwegian-Greenland Sea. The seismic data constrain lithospheric and asthenospheric velocities for lithospheric ages from 0 to 25 Ma. We find lithospheric thickness to closely match the prediction of a simple ridge half-space thermal model (via the temperature and pressure effects on the seismic properties of mantle materials). Asthenospheric shear wave velocities are consistent with this thermal model plus ≤2% melt at the youngest ages. Just at the top of the mantle, a thin zone with velocities intermediate between those of mantle and gabbroic rocks suggests that some melt is frozen into the mantle as might occur if a thin axial lithospheric lid inhibits melt extraction from the mantle and the melt is subsequently frozen into the mantle. If this process occurs to some degree at all slow to very slow spreading ridges, then there may be spatially large reservoirs of unaccounted for gabbroic melt frozen into the mantle throughout many ocean basins.