We report the observation of the intrinsic magnetic susceptibility of highly purified SWCNT samples prepared by a combination of acid treatment and density gradient ultracentrifugation (DGU). We observed that the diamagnetic susceptibility of SWCNTs increases linearly with increasing nanotube diameter. We found that the magnetic susceptibility divided by the diameter is a universal function of the scaled temperature. Furthermore, the estimated magnetic susceptibilities of pure semiconducting and pure metallic SWCNT samples suggest that they respond differently to changes in carrier density, which is consistent with theory. These findings provide experimental verification of the theoretically predicted diameter, temperature, and metallicity dependence of the magnetic susceptibility.