We have studied a Lorentz-violating scalar electrodynamics in which the gauge and scalar fields interact via a nonminimal covariant derivative containing CPT-odd and CPT-even backgrounds. By considering the complex scalar field describes a charged meson we have analyzed the contributions to the mesonic hydrogen energy. By using the experimental data for the 1S strong correction shift and for the pure QED transitions 4P→3P, the best upper-bound for the CPT-odd coupling is <10−3GeV−1 and for the CPT-even one is <10−2GeV−2. Besides, both the nonminimal couplings generate radiative higher-order derivative corrections that are contained in the nonminimal photon sector of the standard model extension. We also have studied their respective contributions to the bound-state energies of the hydrogen-like atoms and determined similar upper-bounds for the Lorentz-violating coefficients.