We show that the Higgs mode of superconductors can couple with spin dynamics in the presence of a static spin-splitting field and Rashba spin-orbit coupling. The Higgs-spin coupling dramatically modifies the spin susceptibility near the superconducting critical temperature and consequently enhances the spin pumping effect in a ferromagnetic insulator/superconductor bilayer system. We show that this effect can be detected by measuring the magnon transmission rate and the magnon-induced voltage generated by the inverse spin Hall effect.