We test the modified Newtonian dynamics (MOND) theory with the velocity dispersion profiles of Galactic globular clusters populating the outermost region of the Milky Way halo, where the Galactic acceleration is lower than the characteristic MOND acceleration a0. For this purpose, we constructed self-consistent, spherical models of stellar systems in MOND, which are the analogues of the Newtonian King models. The models are spatially limited, reproduce well the surface brightness profiles of globular clusters and have velocity dispersion profiles that differ remarkably in shape from the corresponding Newtonian models. We present dynamical models of six globular clusters, which can be used to efficiently test MOND with the available observing facilities. A comparison with recent spectroscopic data obtained for NGC2419 suggests that the kinematics of this cluster might be hard to explain in MOND.