Swift J1644+57 is an unusual transient event, likely powered by the tidal disruption of a star by a massive black hole. Multiple short time-scale X-ray flares were seen over a span of several days. We propose that these flares could be produced by internal shocks. In the internal shock model, the forward and reverse shocks are produced by collisions between relativistic shells ejected from a central engine. The synchrotron emission from the forward and reverse shocks could dominate in two quite different energy bands; under some conditions, the relativistic reverse shock dominates the X-ray emission and the Newtonian forward shock dominates the infrared and optical emission. We show that the spectral energy distribution of Swift J1644+57 could be explained by an internal shock model.