We present radio continuum light curves of the magnetar SGR J1745-2900 and Sgr A∗ obtained with multi-frequency, multi-epoch Very Large Array observations between 2012 and 2014. During this period, a powerful X-ray outburst from SGR J1745-2900 occurred on 2013 April 24. Enhanced radio emission is delayed with respect to the X-ray peak by about seven months. In addition, the flux density of the emission from the magnetar fluctuates by a factor of 2-4 at frequencies between 21 and 41 GHz and its spectral index varies erratically. Here, we argue that the excess fluctuating emission from the magnetar arises from the interaction of a shock generated from the X-ray outburst with the orbiting ionized gas at the Galactic center. In this picture, variable synchrotron emission is produced by ram pressure variations due to inhomogeneities in the dense ionized medium of the Sgr A West bar. The pulsar with its high transverse velocity is moving through a highly blueshifted ionized medium. This implies that the magnetar is at a projected distance of ∼0.1 pc from Sgr A∗ and that the orbiting ionized gas is partially or largely responsible for a large rotation measure detected toward the magnetar. Despite the variability of Sgr A∗ expected to be induced by the passage of the G2 cloud, monitoring data show a constant flux density and spectral index during this period.