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ABSTRACT Magnetic fields provide an important probe of the thermal, material, and structural history of planetary and sub-planetary bodies. Core dynamos are a potential source of magnetic fields for differentiated bodies, but evidence of magnetization in undifferentiated bodies requires a different mechanism. Here, we study the amplified field provided by the stellar wind to an initially unmagnetized body using analytic theory and numerical simulations, employing the resistive magnetohydrodynamic AstroBEAR adaptive mesh refinement multiphysics code. We obtain a broadly applicable scaling relation for the peak magnetization achieved once a wind advects, piles-up, and drapes a body with magnetic field, reaching a quasi-steady state. We find that the dayside magnetic field for a sufficiently conductive body saturates when it balances the sum of incoming solar wind ram, magnetic, and thermal pressures. Stronger amplification results from pile-up by denser and faster winds. Careful quantification of numerical diffusivity is required for accurately interpreting the peak magnetic field strength from simulations, and corroborating with theory. As specifically applied to the Solar system, we find that early solar wind-induced field amplification is a viable source of magnetization for observed paleointensities in meteorites from some undifferentiated bodies. This mechanism may also be applicable to other Solar system bodies, including metal-rich bodies to be visited in future space missions such as the asteroid (16) Psyche.