The high-frequency radio sky is bursting with synchrotron transients from massive stellar explosions and accretion events, but the low-frequency radio sky has, so far, been quiet beyond the Galactic pulsar population and the long-term scintillation of active galactic nuclei. The low-frequency band, however, is sensitive to exotic coherent and polarized radio-emission processes, such as electron-cyclotron maser emission from flaring M dwarfs1, stellar magnetospheric plasma interactions with exoplanets2 and a population of steep-spectrum pulsars3, making Galactic-plane searches a prospect for blind-transient discovery. Here we report an analysis of archival low-frequency radio data that reveals a periodic, low-frequency radio transient. We find that the source pulses every 18.18 min, an unusual periodicity that has, to our knowledge, not been observed previously. The emission is highly linearly polarized, bright, persists for 30-60 s on each occurrence and is visible across a broad frequency range. At times, the pulses comprise short-duration (<0.5 s) bursts; at others, a smoother profile is observed. These profiles evolve on timescales of hours. By measuring the dispersion of the radio pulses with respect to frequency, we have localized the source to within our own Galaxy and suggest that it could be an ultra-long-period magnetar.