The optical transitions of pentacene films deposited on ZnO have been studied by absorption spectroscopy as a function of temperature in the range of room temperature down to 10 K. The pentacene films were prepared with thicknesses of 10 nm, 20 nm, and 100 nm on the ZnO-O(000-1) surface by molecular beam deposition. A unique temperature dependence has been observed for the two Davydov components of the excitons for different film thicknesses. At room temperature, the energetic positions of the respective absorption bands are the same for all films, whereas the positions differ more than 20 meV at 10 K caused by the very different expansion coefficients of pentacene and ZnO. Although the pentacene is just bonded via van der Waals interaction to the ZnO substrate, the very first pentacene monolayer (adlayer) is forced to keep the initial position on the ZnO surface and suffering, therefore, a substantial tensile strain. For all the subsequent pentacene monolayers, the strain is reduced step by step resulting electronically in a strong potential gradient at the interface.