Through polarization-dependent magneto-optical absorption spectroscopy, the magnetic susceptibility anisotropy for metallic single-walled carbon nanotubes has been extracted and found to be up to 4x greater than values for semiconducting single- walled carbon nanotubes. Consistent with theoretical predictions, this is the first experimental evidence of the paramagnetic nature arising from the Aharonov-Bohm-phase-induced gap opening in metallic nanotubes. We also compare our values with previous work for semiconducting nanotubes, which confirm a break from the prediction that the magnetic susceptibility anisotropy increases linearly with the diameter.