The temperature and molecular weight dependence of the self-diffusion coefficient of asymmetric diblock copolymers (polystyrene-b-2-vinylpyridine) (PS-PVP) with a spherical PVP domain structure has been measured by forward recoil spectrometry. The self-diffusion coefficient D is decreased by up to a factor of 10(-4) by the existence of the ordered spherical microstructure. The normalized diffusion coefficient D/D-0, where D-0 is the diffusion coefficient of homopolystyrene with same molecular weight, depends strongly on the product of the interaction parameter chi between PS and PVP and N-PVP, the number of segments in the shorter PVP block, scaling approximately as exp(-1.2 chi N-PVP). Our results suggest that the diffusion process is governed by the thermodynamic barrier for moving PVP blocks from one spherical domain to another in contrast to the normal reptation mechanism seen for homopolymer self-diffusion.