We examine the confinement of induced magnetic fields on the lunar dayside and nightside, when the Moon is in the solar wind. We use a three‐dimensional hybrid model of plasma and place a dipole magnetic field at the center of the Moon to mimic the induced magnetic field, which is the response of the lunar interior to the time‐varying interplanetary magnetic field. Consistent with previous observations and theoretical predictions, we show that the induced magnetic fields on the dayside are confined within the lunar surface through a dayside current sheet. In contrast to previous work, we show that the induced magnetic fields are not confined in the lunar wake, and they leak out, sometimes even appearing as lunar limb compressions. Finally, we identify favorable places to observe induced magnetic fields by electromagnetic sounding techniques, which will help to better constrain the lunar electrical conductivity profile, and interior structure.