In this work, a novel mechanism for spontaneous symmetry breaking is presented. This mechanism incorporates gravity in the generation of masses for gauge fields, showing that the Higgs mechanism can take place even without a quartic self-interaction at the fundamental level. Using the scale-dependent effective action Γk minimally coupled to a gravitational sector, a variational parameter setting is applied. This provides a mass and vacuum expectation value as a function of the constants arising in the low-scale expansion of Newton and cosmological couplings. A comparison with experimental data, such as the Higgs mass, allows putting restrictions on these constants. This generic approach can be compared with explicit candidates for an effective field theory of gravity. As an example, we use the asymptotic safety scenario, where we find restrictions on the matter content of the theory.