Abstract This study provides first observational evidence of a plasma wake behind ESA’s Swarm satellites, manifesting itself by a brief magnetic field strength spike and bipolar field variations in transverse direction. These magnetic signatures occur only near the dip‐equator where the magnetic declination is close to zero. Their amplitudes are proportional to the ambient electron density. We suggest that such magnetic field disturbances are caused by a trailing flux rope that passes the magnetometers. We regard plasma density‐gradient currents on the fringes of the wake behind Swarm as cause for the enhanced ambient field strength. Thermal electrons are assumed to populate the wake, but they are retarded by an ambipolar electric field. This E‐field, pointing primarily inward and in flight direction, may well be the driver of the additional field‐aligned current. Although the spurious signals are not large (<0.5 nT), they may have disturbing effects because of their sytematic appearance.