We perform molecular dynamics simulations to understand the translational and rotational diffusion of Janus nanoparticles at the interface between two immiscible fluids. Considering spherical particles with different affinity to fluid phases, both their dynamics as well as the fluid structure around them are evaluated as a function of particle size, amphiphilicity, fluid density, and interfacial tension. We show that as the particle amphiphilicity increases due to enhanced wetting of each side with its favorite fluid, the rotational thermal motion decreases. Moreover, the in-plane diffusion of nanoparticles at the interface becomes slower for more amphiphilic particles, mainly due to the formation of a denser adsorption layer. The particles induce an ordered structure in the surrounding fluid that becomes more pronounced for highly amphiphilic nanoparticles, leading to increased resistance against nanoparticle motion. A similar phenomenon is observed for homogeneous particles diffusing in bulk upon increasing their wettability. Our findings can provide fundamental insight into the dynamics of drugs and protein molecules with anisotropic surface properties at biological interfaces including cell membranes.