Stress-driven migration of grain boundaries (GBs) is theoretically described as a plastic deformation mode in metal matrix nanocomposites containing incoherent reinforcing (ceramic or metallic) nanoinclusions. We considered the exemplary case of low-angle tilt boundaries migrating in nanocrystalline or ultrafine-grained metallic matrixes and analytically calculated the effects of reinforcing nanoinclusions on the GB migration process. In doing so, migrating low-angle tilt boundaries are represented as walls of edge lattice dislocations that cooperatively glide in a metal matrix but cannot penetrate wire nanoinclusions. It is theoretically revealed that the nanoinclusions typically hamper the stress-driven GB migration. At the same time, in the situation with small (ultrafine) nanoinclusions, they cause an anomalous effect enhancing (or, in other terms, decreasing the critical stress for unlimited migration) the stress-driven GB migration in metal-metal and metal-ceramic nanocomposites. The results of our theoretical examination are consistent with the corresponding experimental data reported in the literature.