Single-cycle terahertz fields generated by coherent transition radiation from a relativistic electron beam are used to study the high field optical response of single crystal GaAs. Large amplitude changes in the sub-band-gap optical absorption are induced and probed dynamically by measuring the absorption of a broad-band optical beam generated by transition radiation from the same electron bunch, providing an absolutely synchronized pump and probe geometry. This modification of the optical properties is consistent with strong-field-induced electroabsorption. These processes are pertinent to a wide range of nonlinear terahertz-driven light-matter interactions anticipated at accelerator-based sources.