The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will soon start imaging thousands of square degrees of the northern sky with its unique set of 56 filters (spectral resolution of R ∼ 60). Before the arrival of the final instrument, we observed 1 deg2 on the AEGIS field with an interim camera with all the J-PAS filters. Taking advantage of these data, dubbed miniJPAS, we aim at proving the scientific potential of the J-PAS to derive the stellar population properties of galaxies via fitting codes for spectral energy distributions (SEDs), with the ultimate goal of performing galaxy evolution studies across cosmic time. One parametric (BaySeAGal) and three non-parametric (MUFFIT, AlStar, and TGASPEX) SED-fitting codes are used to constrain the stellar mass, age, metallicity, extinction, and rest-frame and dust-corrected (u ‒ r) colours of a complete flux-limited sample (rSDSS ≤ 22.5 AB) of miniJPAS galaxies that extends up to z = 1. We generally find consistent results on the galaxy properties derived from the different codes, independently of the galaxy spectral type or redshift; this is remarkable considering that 25% of the J-spectra have signal-to-noise ratios (S/N) ∼3. For galaxies with S/N ≥ 10, we estimate that the J-PAS photometric system will allow us to derive the stellar population properties of rest-frame (u ‒ r) colour, stellar mass, extinction, and mass-weighted age with a precision of 0.04 ± 0.02 mag, 0.07 ± 0.03 dex, 0.2 ± 0.09 mag, and 0.16 ± 0.07 dex, respectively. This precision is equivalent to that obtained with spectroscopic surveys of similar S/N. By using the dust-corrected (u ‒ r) colour-mass diagram, a powerful proxy for characterizing galaxy populations, we find: (i) that the fraction of red and blue galaxies evolves with cosmic time, with red galaxies being ∼38% and ∼18% of the whole population at z = 0.1 and z = 0.5, respectively, and (ii) consistent results between codes for the average intrinsic (u ‒ r) colour, stellar mass, age, and stellar metallicity of blue and red galaxies and their evolution up to z = 1. At all redshifts, the more massive galaxies belong to the red sequence, and these galaxies are typically older and more metal-rich than their counterparts in the blue cloud. Our results confirm that with J-PAS data we will be able to analyse large samples of galaxies up to z ∼ 1, with galaxy stellar masses above log(M⋆/M⊙)∼8.9, 9.5, and 9.9 at z = 0.3, 0.5, and 0.7, respectively. The star formation history of a complete sub-sample of galaxies selected at z ∼ 0.1 with log(M⋆/M⊙) > 8.3 constrains the cosmic evolution of the star formation rate density up to z ∼ 3, in good agreement with results from cosmological surveys.