Hydrodynamic interactions in complex fluids are investigated by the multi-particle-collision-dynamics algorithm, a mesoscopic simulation technique. The diffusive dynamics of simple fluids is studied, and the diffusion coefficient is calculated as a function of the mean free path of a particle. For small mean free paths, we observe strong effects due to hydrodynamic interactions among the fluid particles. These results are then used to study the dynamics of short polymer chains in solution. For an appropriate choice of the mean free path of the solvent, we obtain excellent agreement of our simulation results with the predictions of Zimm theory for the center-of-mass diffusion coefficient and the relaxation times of the Rouse modes.