MiniJPAS is a ~1 deg^2 imaging survey of the AEGIS field in 60 bands, performed to demonstrate the scientific potential of the upcoming JPAS survey. Full coverage of the 3800-9100 AA range with 54 narrow and 6 broad optical filters allow for extremely accurate photo-z, which applied over 1000s of deg^2 will enable new applications of the photo-z technique such as measurement of baryonic acoustic oscillations. In this paper we describe the method used to obtain the photo-z included in the publicly available miniJPAS catalogue, and characterise the photo-z performance. We build 100 AA resolution photo-spectra from the PSF-corrected forced-aperture photometry. Systematic offsets in the photometry are corrected by applying magnitude shifts obtained through iterative fitting with stellar population synthesis models. We compute photo-z with a customised version of LePhare, using a set of templates optimised for the J-PAS filter-set. We analyse the accuracy of miniJPAS photo-z and their dependence on multiple quantities using a subsample of 5,266 galaxies with spectroscopic redshifts from SDSS and DEEP, that we find to be representative of the whole r<23 miniJPAS sample. Formal uncertainties for the photo-z that are calculated with the deltachi^2 method underestimate the actual redshift errors. The odds parameter has the stronger correlation with |Dz|, and accurately reproduces the probability of a redshift outlier (|Dz|>0.03) irrespective of the magnitude, redshift, or spectral type of the sources. We show that the two main summary statistics characterising the photo-z accuracy for a population of galaxies (snmad and eta) can be predicted by the distribution of odds in such population, and use this to estimate them for the whole miniJPAS sample. At r<23 there are 17,500 galaxies/deg^2 with valid photo-z estimates, of which 4,200 are expected to have |Dz|<0.003 (abridged).
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