We present an infrared spectroscopy study of ZrTe5, which confirms a recent theoretical proposal that this material exhibits a temperature-driven topological quantum phase transition from a weak to a strong topological insulating state with an intermediate Dirac semimetal state around Tp ≃ 138 K. Our study details the temperature evolution of the energy gap in the bulk electronic structure. We found that the energy gap closes around Tp, where the optical response exhibits characteristic signatures of a Dirac semimetal state, i.e., a linear frequency-dependent optical conductivity extrapolating to the origin (after subtracting a weak Drude response). This finding allows us to reconcile previous diverging reports about the topological nature of ZrTe5 in terms of a variation of Tp that depends on the crystal growth condition.