The discovery of neutrino masses has raised the importance of studies in the context of neutrinoless double beta decay (0νββ), which constitutes a landmark for lepton number violation (LNV). The standard interpretation is that the light massive neutrinos, that we observed oscillating in terrestrial experiments, mediate double beta decay. In the minimal 3-3-1 model (3-3-1M), object of our study, there is an additional contribution that stems from the mixing between a new charged vector boson, W , and the Standard Model W boson. Even after setting this mixing to be very small, we show that tight constraints arise from the non-observation of (0νββ). Indeed, we derive bounds on the mass of the W gauge boson that might exceed those from collider probes, and most importantly push the scale of symmetry breaking beyond its validity, leading to an exclusion bound for the minimal 3-3-1 model.