We report a new nonlocal effect in vortex matter, where an electric current confined to a small region of a long and sufficiently narrow superconducting wire causes vortex flow at distances hundreds of intervortex separations away. The observed remote traffic of vortices is attributed to a very efficient transfer of a local strain through the one-dimensional vortex lattice (VL), even in the presence of disorder. We also observe mesoscopic fluctuations in the nonlocal vortex flow, which arise due to "traffic jams" when vortex arrangements do not match a local geometry of a superconducting channel.