The combination of high-resolution and sensitivity offered by ALMA is revolutionizing our understanding of protoplanetary discs, as their bulk gas and dust distributions can be studied independently. In this paper we present resolved ALMA observations of the continuum emission (λ = 1.3 mm) and CO isotopologues (12CO, 13CO, C18O, J = 2 ？ 1) integrated intensity from the disc around the nearby (d = 162 pc), intermediate-mass (？M？=1.67M⊙？) pre-main-sequence star CQ Tau. The data show an inner depression in continuum and in both 13CO and C18O emission. We employ a thermo-chemical model of the disc reproducing both continuum and gas radial intensity profiles, together with the disc spectral energy distribution. The models show that a gas inner cavity with size between 15 and 25 au is needed to reproduce the data with a density depletion factor between ∼10？1 and ∼10？3. The radial profile of the distinct cavity in the dust continuum is described by a Gaussian ring centred at Rdust=53au and with a width of σ=13au. Three-dimensional gas and dust numerical simulations of a disc with an embedded planet at a separation from the central star of ∼20 au and with a mass of ∼6？9MJup reproduce qualitatively the gas and dust profiles of the CQ Tau disc. However, a one-planet model appears not to be able to reproduce the dust Gaussian density profile predicted using the thermo-chemical modeling.