We use a novel measure of shape complexity known as configurational entropy to obtain stability bounds of various astrophysical objects. We apply the method to Newtonian polytropes, neutron stars with an Oppenheimer-Volkoff equation of state, and to self-gravitating configurations of complex scalar field (boson star) in ground and excited states. The versatility of this method has also been tested on hydrogen atom in comparison with boson stars. Configurational entropic measure locates critical stability regions obtained from perturbation method with accuracy of a few percent or better.