Context. The eclipsing binary GU Mon is located in the star-forming cluster Dolidze 25, which has the lowest metallicity measured in a Milky Way young cluster. Aims: GU Mon has been identified as a short-period eclipsing binary with two early B-type components. We set out to derive its orbital and stellar parameters. Methods: We present a comprehensive analysis, including B and V light curves and 11 high-resolution spectra, to verify the orbital period and determine parameters. We used the stellar atmosphere code FASTWIND to obtain stellar parameters and create templates for cross-correlation. We obtained a model to fit the light and radial-velocity curves using the Wilson-Devinney code iteratively and simultaneously. Results: The two components of GU Mon are identical stars of spectral type B1 V with the same mass and temperature. The light curves are typical of an EW-type binary. The spectroscopic and photometric analyses agree on a period of 0.896640 ± 0.000007 d. We determine a mass of 9.0 ± 0.6 M⊙ for each component and for temperatures of 28 000 ± 2000 K. Both values are consistent with the spectral type. The two stars are overfilling their respective Roche lobes, sharing a common envelope and, therefore the orbit is synchronised and circularised. Conclusions: The GU Mon system has a fill-out factor above 0.8, containing two dwarf B-type stars on the main sequence. The two stars are in a very advanced stage of interaction, with their extreme physical similarity likely due to the common envelope. The expected evolution of such a system very probably leads to a merger while still on the main sequence. Photometry tables are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/590/A45