We present the results of optical (R band) photometric and polarimetric monitoring and Very Long Baseline Array (VLBA) imaging of the blazar S5 0716+714 along with Fermi gamma-ray data during a multi-waveband outburst in 2011 October. We analyze total and polarized intensity images of the blazar obtained with the VLBA at 43 GHz during and after the outburst. Monotonic rotation of the linear polarization vector at a rate of greater than or similar to 50 degrees per night coincided with a sharp maximum in gamma-ray and optical flux. At the same time, within the uncertainties, a new superluminal knot appeared with an apparent speed of 21 +/- 2c. The general multi-frequency behavior of the outburst can be explained within the framework of a shock wave propagating along a helical path in the blazar's jet.