We present results from the most comprehensive radio monitoring campaign towards the closest star to our Sun, Proxima Centauri. We report 1.1–3.1 GHz observations with the Australia Telescope Compact Array over 18 consecutive days in April 2017. We detected radio emission from Proxima Centauri for most of the observing sessions, which spanned ~1.6 orbital periods of the planet Proxima b. The radio emission is stronger at the low-frequency band, centered around 1.6 GHz, and is consistent with the expected electron-cyclotron frequency for the known star’s magnetic field intensity of ~600 gauss. The 1.6 GHz light curve shows an emission pattern that is consistent with the orbital period of the planet Proxima b around the star Proxima, with its maxima of emission happening near the quadratures. We also observed two short-duration flares (a few minutes) and a long-duration burst (about three days) whose peaks happened close to the quadratures. We find that the frequency, large degree of circular polarization, change in the sign of circular polarization, and intensity of the observed radio emission are all consistent with expectations from electron cyclotron-maser emission arising from sub-Alfvénic star–planet interaction. We interpret our radio observations as signatures of interaction between the planet Proxima b and its host star Proxima. We advocate for monitoring other dwarf stars with planets to eventually reveal periodic radio emission due to star–planet interaction, thus opening a new avenue for exoplanet hunting and the study of a new field of exoplanet–star plasma interaction.