The magnetic susceptibility of the QCD vacuum is analyzed in the framework of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model. Considering two different model parametrizations, we estimate the values of the u- and s-quark tensor coefficients and magnetic susceptibilities and then we extend the analysis to finite temperature systems. Our numerical results are compared to those obtained in other theoretical approaches and in lattice QCD calculations.