We propose a four-quark structure for some of the excited states of heavy mesons containing a single charm or bottom quark. The four-quark wave functions are constructed based on a diquark-antidiquark form under the constraint that they form an antitriplet ${\overline{\mathbf{3}}}_f$ in ${\mathrm{SU}(3)}_f$, which seems to be realized in some of the excited states listed by the Particle Data Group. Depending on the structure of the antidiquark, we construct two possible models for its wave functions: Model I, where the antidiquark is symmetric in flavor (${\overline{\mathbf{6}}}_f$) and antisymmetric in color (${\mathbf{3}}_c$), and Model II, where the antidiquark is antisymmetric in flavor (${\mathbf{3}}_f$) and symmetric in color (${\overline{\mathbf{6}}}_c$). To test the phenomenological relevance of these wave functions, we calculate the mass differences among the excited states of spin $J=0$, 1, 2 using color-spin interactions. The four-quark wave functions based on Model I are found to reproduce the observed mass of the excited states of heavy mesons. Also, our four-quark model provides an interesting phenomenology related to the decay widths of the excited states. To further pursue the possibility of the four-quark structure, we make a few predictions for open-charm and open-bottom states that may be discovered in future experiments. Most of these are expected to have broad widths, which would make them difficult to be identified experimentally. However, one resonance with $J=1$ containing bottom and strange quarks is expected to appear as a sharp peak with a mass around $B_{1N}^{\overline{s}}\sim 5753\mathrm{MeV}$. The confirmation of the existence of such states in future experiments will shed light on our understanding of the structure of heavy meson excited states.