  We consider an impact of hadronic light-by-light scattering on the muonium
hyperfine structure. A shift of the hyperfine interval $\Delta \nu({\rm Mu})
_{\rm\tiny HLBL}$ is calculated with the light-by-light scattering approximated
by exchange of pseudoscalar and pseudovector mesons. Constraints from the
operator product expansion in QCD are used to fix parameters of the model
similar to the one used earlier for the hadronic light-by-light scattering in
calculations of the muon anomalous magnetic moment. The pseudovector exchange
is dominant in the resulting shift, $\Delta \nu({\rm Mu})_{\rm\tiny HLBL}=
-0.0065(10) {Hz}$. Although the effect is tiny it is useful in understanding
the level of hadronic uncertainties.
