Variable sources probe a wide range of astrophysical phenomena. We present a catalogue of over 10 million variable source candidates found in Data Release 1 (DR1) of the Zwicky Transient Facility (ZTF). We perform a periodicity search up to a frequency of 160 d-1, and we classify the light curves into erratic and smooth variables.We also present variability indicators and the results of a periodicity search, up to a frequency of 5 d-1, for about 1 billion sources in the ZTF-DR1 light curve data base. We present several new short-period (<90 min) candidates, and about 60 new dwarf nova candidates, including two candidate eclipsing systems. Both the 10 million variables catalogue and ∼1 billion source catalogue are available online in catsHTM format.