The recent discovery of the G2 cloud of dense, ionized gas on a trajectory toward Sgr A*, the black hole at the dynamical center of the Galaxy, offers a unique opportunity to observe an accretion event onto a massive black hole as well as to probe its immediate environment. Simulations and models predict increased X-ray and radio variability resulting from increased accretion driven by drag on an atmosphere of hot, X-ray-emitting gas surrounding Sgr A*. Here, we present X-ray and radio light curves of the emission resulting from the potential encounter of the G2 cloud with a relativistic jet from Sgr A*. This interaction would violently shock a portion of the G2 cloud to temperatures ∼108 K, resulting in bright X-ray emission from the dense, shocked gas as it adiabatically expands. The 2-10 keV luminosity may reach ∼10 times the quiescent X-ray flux of Sgr A*. Approximately 3 LȮ is emitted above 10 keV at the peak of the light curve, with significant softening of the spectrum occurring as the gas subsequently cools. Observations with NuSTAR would therefore be able to confirm such an event as well as determine the cloud speed. At radio wavelengths, the associated synchrotron radio emission may reach levels of a few jansky.