We have used multiple mid-infrared observations at 4.5 micron obtained with the Infrared Array Camera, of the compact (~1.4 arcmin) young stellar bipolar outflow Cep E to measure the proper motion of its brightest condensations. The images span a period of ~6 yr and have been reprocessed to achieve a higher angular resolution (~0.8 arcsec) than their normal beam (2 arcsec). We found that for a distance of 730 pc, the tangential velocities of the North and South outflow lobes are 62+/-29 and 94+/-6 km/s respectively, and moving away from the central source roughly along the major axis of the flow. A simple 3D hydrodynamical simulation of the H2 gas in a precessing outflow supports this idea. Observations and model confirm that the molecular Hydrogen gas, traced by the pure rotational transitions, moves at highly supersonic velocities without being dissociated. This suggests either a very efficient mechanism to reform H2 molecules along these shocks or the presence of some other mechanism (e.g. strong magnetic field) that shields the H2 gas.