Global observations of mid-ocean ridge (MOR) bathymetry demonstrate an asymmetry in axial depth across ridge offsets that is correlated with the direction of ridge migration. Motivated by these observations, we have developed two-dimensional numerical models of asthenospheric flow and melting beneath a migrating MOR. The modification of the flow pattern produced by ridge migration leads to an asymmetry in melt production rates on either side of the ridge. By coupling a simple parametric model of three dimensional melt focusing to our simulations, we generate predictions of axial depth differences across offsets in the MOR. These predictions are quantitatively consistent with the observed asymmetry.