We report on the measurement of the contribution of the magnetic-dipole hyperfine interaction to the tensor polarizaility of the electronic ground state in ^{87}Rb. This contribution was isolated by measuring the differential shift of the clock transition frequency in ^{87}Rb atoms that were optically trapped in the focus of an intense CO_{2} laser beam. By comparing to previous tensor polarizability measurements in ^{87}Rb, the contribution of the interaction with the nuclear electric-quadrupole moment was isolated as well. Our measurement will enable better estimation of blackbody shifts in Rb atomic clocks. The methods reported here are applicable for future spectroscopic studies of atoms and molecules under strong quasistatic fields.