Cavity magnomechanics, leveraging magnetostrictive interactions, has emerged as an important platform for implementing spinbased precision measurement and investigating macroscopic quantum phenomena. Due to the weakness of the intrinsic magnetostrictive effect, the coupling between magnetic and mechanical vibrations in typical magnomechanical systems is relatively small. Here, we develop a center-of-mass magnomechanical system that is non-reliant on magnetostrictive effects. The proposed system consists of an inhomogeneous magnetic field and a yttrium iron garnet(YIG) sphere that is harmonically confined. We theoretically investigate the interaction between center-of-mass motion and magnonic excitation of the YIG sphere, and find that the field inhomogeneity induces a static force on the YIG sphere. Consequently, a magnomechanical interaction between the center-of-mass motion and the magnonic excitation is established. The parameter optimization of the magnomechanical interaction has been performed, and we show that the proposed system has the potential to reside in both the single-magnon high-cooperativity regime and the sideband-resolved regime. The capabilities of the system for magnomechanical applications,such as ground-state cooling of the mechanical mode, have been discussed, and we show that ground-state cooling of the mechanical mode is feasible in the unresolved sideband regime by taking into account the magnonics Kerr effect. Our analysis holds great promise for achieving magnonic nonlinearity at low excitation levels, thereby opening up avenues for magnomechanical applications in precision measurements and quantum manipulation.