A theoretical study of photoinduced heterogeneous electron transfer in the dye-semiconductor system coumarin 343-TiO2 is presented. The study is based on a generic model for heterogeneous electron transfer reactions, which takes into account the coupling of the electronic states to the nuclear degrees of freedom of coumarin 343 as well as to the surrounding solvent. The quantum dynamics of the electron injection process is simulated employing the recently proposed multilayer formulation of the multiconfiguration time-dependent Hartree method. The results reveal an ultrafast injection dynamics of the electron from the photoexcited donor state into the conduction band of the semiconductor. Furthermore, the mutual influence of electronic injection dynamics and nuclear motion is analyzed in some detail. The analysis shows that-depending on the time scale of nuclear motion-electronic vibrational coupling can result in electron transfer driven by coherent vibrational motion or vibrational motion induced by ultrafast electron transfer.