It is widely believed that the mechanism for spin pumping in ferromagnet-nonmagnet bilayers is the exchange interaction between the ferromagnet and nonmagnetic material. We observe 1000-fold exponential decay of spin pumping from thin Y3Fe5O12 films to Pt across insulating barriers, from which exponential decay lengths of 0.16, 0.19, and 0.23 nm are extracted for oxide barriers having band gaps of 4.91, 3.40, and 2.36 eV, respectively. This archetypal signature of quantum tunneling through a barrier underscores the importance of exchange coupling for spin pumping and reveals its dependence on the characteristics of the barrier material.