The diffusion of monomerically thin nanorods in polymer melts is studied by molecular dynamics simulations. We focus on the systems where chains are long enough to screen the hydrodynamic interactions such that the diffusion coefficient D ∥ for the direction parallel to the rod decreases linearly with increasing rod length l. In unentangled polymers, the diffusion coefficient for the direction normal to the rod exhibits a crossover from D ⊥ ~ l -2 to D ⊥ ~ l -1 with increasing l, corresponding to a progressive coupling of nanorod motion to the polymers. Accordingly, the rotational diffusion coefficient D R ≈ D ⊥ l -2 ~ l -4 and then D R ~ l -3 as l increases. In entangled polymers, D ⊥ and D R are suppressed for l larger than the entanglement mesh size a. D ⊥ ~ l -3 and D R ~ l -5 for l sufficiently above a in agreement with de Gennes' rod reptation model.