A force acting on a nanoparticle occurring in a fluid has been studied by the molecular dynamics method. It is shown that this force is nonstationary and exhibits a relaxation character. At the initial instant, it is two to three times the Stokes force, but then decreases and, outside the first relaxation region, becomes smaller than the Stokes force. A stationary force acting on a nanoparticle is determined by the particle mass and size. Correlation expressions for determining the drag coefficient are constructed. It is established that the drag force is anisotropic.