We investigate the electronic structure of carbon nanotubes functionalized by adsorbates anchored with single C-C covalent bonds. We find that despite the particular adsorbate, a spin moment with a universal value of 1.0 μB per molecule is induced at low coverage. Therefore, we propose a mechanism of bonding-induced magnetism at the carbon surface. The adsorption of a single molecule creates a dispersionless defect state at the Fermi energy, which is mainly localized in the carbon wall and presents a small contribution from the adsorbate. This universal spin moment is fairly independent of the coverage as long as all the molecules occupy the same graphenic sublattice. The magnetic coupling between adsorbates is also studied and reveals a key dependence on the graphenic sublattice adsorption site.