We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we present explicitly a given a set of non jointly measurable POVMs MA with the following property. Considering a bipartite Bell test where Alice uses MA, then for any possible shared entangled state ρ and any set of (possibly infinitely many) POVMs NB performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.