High-intensity coherent light can realize hybrid phases of matter that are not accessible in equilibrium. The coherent interaction between Bloch states and a periodic electric field, which leads to Floquet-engineered band structures, has been extensively discussed in the literature and shown to enable modified electronic states, and it potentially induces topological phases in semiconductors. However, a Floquet topological insulator has not yet been realized experimentally in a semiconductor. Here we show that femtosecond light pulses can create a short-lived topological state in SnTe that is absent from the equilibrium ground state. This occurs when the photo-excitation energy is close to the bandgap of this polar semiconductor. We observe a concomitant renormalization of the band dispersions that reveals the generation of Floquet states connected to the topological state. These results provide a direct experimental observation of a Floquet topological state and indicate that it is driven by a light-induced band inversion in SnTe, although further theoretical work will provide a more detailed characterization of the state. Our work also indicates that optical control of the topological properties of semiconductors on demand is possible.