Entangling superconducting quantum processors via light would enable new means of secure communication and distributed quantum computing. However, transducing quantum signals between these disparate regimes of the electromagnetic spectrum remains an outstanding goal, and interfacing superconducting qubits with electro-optic transducers presents significant challenges due to the deleterious effects of optical photons on superconductors. Moreover, many remote entanglement protocols require multiple qubit gates both preceding and following the upconversion of the quantum state, and thus an ideal transducer should leave the state of the qubit unchanged: more precisely, the backaction from the transducer on the qubit should be minimal. Here we demonstrate non-destructive optical readout of a superconducting transmon qubit via a continuously operated electro-optic transducer. The modular nature of the transducer and circuit QED system used in this work enable complete isolation of the qubit from optical photons, and the backaction on the qubit from the transducer is less than that imparted by thermal radiation from the environment. Moderate improvements in transducer bandwidth and added noise will enable us to leverage the full suite of tools available in circuit QED to demonstrate transduction of non-classical signals from a superconducting qubit to the optical domain.