By using the quantized Fresnel modes in the planar cavity, the resonant molecular interaction is theoretically described and the general interaction potential tensor is obtained. The resonant dipole-dipole (D-D) interaction or excitation transfer matrix element are found to be dramatically suppressed or enhanced by the surrounding planar boundaries. The analytic expressions of the resonant D-D interaction potential are obtained for a few limiting cases. The results thus obtained are closely related to various phenomena associated with the spatial confinement, such as confinement-induced phase transitions of liquids, resonant excitation transfer between molecules bound in membrane etc. In the case of the high-Q cavity, the reduction of the effective dimensionality is discussed. Secondly, the short-distance limit of the general resonant molecular interaction potential tensor and its frequency dependence are investigated. Numerical calculations of the high-Q cavity limit and the lipid-water system are presented to demonstrate the crucial role of the planar boundaries in the resonant D-D interaction. The relevances of the current investigation with the excitation transfer in the photosynthetic antenna system, coherent energy transfer between neighboring peptide bonds, and static D-D interaction in the molecular dynamics simulation study of the membrane-bound proteins are briefly discussed.