Many lines of reasoning suggest that external galaxies should host planetary systems, but detecting them by methods typically used in our own Galaxy is not possible. An alternative approach is to study the temporal behaviour of X-rays emitted by bright extragalactic X-ray sources, where an orbiting planet would temporarily block the X-rays and cause a brief eclipse. We report on such a potential event in the X-ray binary M51-ULS-1 in the galaxy M51. We examined a range of explanations for the observed X-ray dip, including a variety of transiting objects and enhancements in the density of gas and dust. The latter are ruled out by the absence of changes in X-ray colours, save any with sharp density gradients that cannot be probed with our data. Instead, the data are well fit by a planet transit model in which the eclipser is most likely to be the size of Saturn. We also find that the locations of possible orbits are consistent with the survival of a planet bound to a mass-transfer binary.