We present an infrared spectroscopy study of ZrTe_{5}, 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 T_{p}≃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 T_{p}, 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 ZrTe_{5} in terms of a variation of T_{p} that depends on the crystal growth condition.