This Letter describes the first application of entanglement-induced virtual-state spectroscopy to a molecular system. Non-classical, non-monotonic behaviour in the two-photon absorption cross-section of the OH A-X system, induced by entangled photon pairs is theoretically demonstrated. A Fourier transform analysis of the biphoton cross-section permits access to the energy eigenvalues of intermediate rovibronic states with a fixed excitation energy. Our analysis reveals that the implementation of virtual-state spectroscopy of the OH A-X system requires tuning of the relative path delay tau(e) over a picosecond range with ferntosecond resolution for a certain entanglement time T-e. (C) 2004 Elsevier B.V. All rights reserved.