Analyses of lunar samples suggest the Moon once possessed a dynamo from ~4.25 Ga until perhaps as recently as 1 Ga, with surface field strengths between ~5 and 100 μT. While the exact timing, strength, and structure of these paleomagnetic fields are not precisely known, such relatively strong fields imply that the Moon also likely possessed a magnetosphere. Here, we present hybrid plasma simulations of the structure and morphology of the putative lunar “paleo‐magnetosphere” for varying surface field strengths and orientations, using ambient solar wind conditions representative of the early Sun. The presence of the paleo‐magnetosphere reduces total solar wind fluxes to the lunar surface overall yet, for a spin‐aligned dynamo, increases the relative solar wind flux to the lunar polar regions. In turn, the paleo‐magnetosphere may have altered the rate of volatile accretion to the Moon over its history.