Hybrid quantum optomechanical systems interface a single two-level system with a macroscopic mechanical degree of freedom. In a microwire with a single embedded semiconductor quantum dot, not only can the wire vibration modulate the excitonic transition energy, but the optical drive of the quantum dot can also induce motion in the wire. Hybrid quantum optomechanical systems(1) interface a macroscopic mechanical degree of freedom with a single two-level system such as a single spin(2-4), a superconducting qubit(5-7) or a single optical emitter(8-12). Recently, hybrid systems operating in the microwave domain have witnessed impressive progress(13,14). Concurrently, only a few experimental approaches have successfully addressed hybrid systems in the optical domain, demonstrating that macroscopic motion can modulate the two-level system transition energy(9,10,15). However, the reciprocal effect, corresponding to the backaction of a single quantum system on a macroscopic mechanical resonator, has remained elusive. In contrast to an optical cavity, a two-level system operates with no more than a single energy quantum. Hence, it requires a much stronger hybrid coupling rate compared to cavity optomechanical systems(1,16). Here, we build on the large strain coupling between an oscillating microwire and a single embedded quantum dot(9). We resonantly drive the quantum dot's exciton using a laser modulated at the mechanical frequency. State-dependent strain then results in a time-dependent mechanical force that actuates microwire motion. This force is almost three orders of magnitude larger than the radiation pressure produced by the photon flux interacting with the quantum dot. In principle, the state-dependent force could constitute a strategy to coherently encode the quantum dot quantum state onto a mechanical degree of freedom(1).