Context. Quantifying the number, type, and distribution of Wolf-Rayet (W-R) stars is a key component in the context of galaxy evolution, since they put constraints on the age of the star formation bursts. Nearby galaxies (distances ≲5 Mpc) are particularly relevant in this context since they fill the gap between studies in the Local Group, where individual stars can be resolved, and galaxies in the Local Volume and beyond. Aims: We intend to characterise the W-R star population in one of these systems, NGC 625, which is a low-metallicity dwarf galaxy suffering a currently declining burst of star formation. Methods: Optical integral field spectroscopy (IFS) data have been obtained with the VIMOS-IFU and the HR_Orange and HR_Blue gratings at the Very Large Telescope covering the starburst region of NGC 625. Ancillary Hubble Space Telescope (HST) images in the F555W and F814W bands are also used for comparison. We estimate the number of W-R stars using a linear combination of three W-R templates: one early-type nitrogen (WN) star, one late-type WN star, and one carbon-type (WC) star (or oxygen-type (WO) star). Fits using several ensembles of templates were tested. Results were confronted with i) high spatial resolution HST photometry; ii) numbers of W-R stars in nearby galaxies; and iii) model predictions. Results: The W-R star population is spread over the main body of the galaxy and is not necessarily coincident with the overall stellar distribution. Our best estimation for the number of W-R stars yields a total of 28 W-R stars in the galaxy, out of which 17 are early-type WN, six are late-type WN, and five are WC stars. The width of the stellar features nicely correlates with the dominant W-R type found in each aperture. The distribution of the different types of WR in the galaxy is roughly compatible with the way star formation has propagated in the galaxy, according to previous findings using high spatial resolution with the HST. Fits using templates at the metallicity of the Large Magellanic Cloud yield more reasonable number of W-R than those using templates at the metallicity of the Small Magellanic Cloud. Given the metallicity of NGC 625, this suggests a non-linear relation between the metallicity and luminosity of the W-R spectral features.