We describe an adiabatic state transfer mechanism that allows for high-fidelity transfer of a microwave quantum state from one cavity to another through an optical fiber. The conversion from microwave frequency to optical frequency is enabled by an optomechanical transducer. The transfer process utilizes a combined dark state of the mechanical oscillator and fiber modes, making it robust against both mechanical and fiber loss. We anticipate this scheme being an enabling component of a hybrid quantum computing architecture consisting of superconducting qubits with optical interconnects.