We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton’s constant is allowed to vary with the radial coordinate throughout the star. Assuming (1) a linear equation-of-state in the MIT bag model for quark matter, and (2) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton’s constant throughout the objects leads to slightly more massive and more compact stars.