We present the results of a photometric search for variable stars in the core of the Galactic globular cluster Messier 4 (M 4). The input data are a large and unprecedented set of deep Hubble Space Telescope WFC3 images (large programme GO-12911; 120 orbits allocated), primarily aimed at probing binaries with massive companions by detecting their astrometric wobbles. Though these data were not optimized to carry out a time-resolved photometric survey, their exquisite precision, spatial resolution and dynamic range enabled us to firmly detect 38 variable stars, of which 20 were previously unpublished. They include 19 cluster-member eclipsing binaries (confirming the large binary fraction of M 4), RR Lyrae and objects with known X-ray counterparts. We improved and revised the parameters of some among published variables.