In this work we will test an alternative model of gravity belonging to the large family of Galileon models. It is characterized by an intrinsic breaking of the Vainshtein mechanism inside large astrophysical objects, thus having possibly detectable observational signatures. We will compare theoretical predictions from this model with the observed total mass profile for a sample of clusters of galaxies. The profiles are derived using two complementary tools: x-ray hot intracluster gas dynamics, and strong and weak gravitational lensing. We find that a dependence with the dynamical internal status of each cluster is possible; for those clusters which are very close to be relaxed, and thus less perturbed by possible astrophysical local processes, the Galileon model gives a quite good fit to both x-ray and lensing observations. Both masses and concentrations for the dark matter halos are consistent with earlier results found in numerical simulations and in the literature, and no compelling statistical evidence for a deviation from general relativity is detectable from the present observational state. Actually, the characteristic Galileon parameter ϒ is always consistent with zero, and only an upper limit (≲0.086 at 1 σ , ≲0.16 at 2 σ , and ≲0.23 at 3 σ ) can be established. Some interesting distinctive deviations might be operative, but the statistical validity of the results is far from strong, and better data would be needed in order to either confirm or reject a potential tension with general relativity.