degree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we realize a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum interference of the superconducting phase across the tunnel junctions. We demonstrate a vacuum electromechanical coupling rate up to 4 kHz by making the transmon qubit resonant with the readout cavity. Consequently, thermal-motion of the mechanical resonator is detectable by driving the dressed-mode with mean-occupancy well below one photon. By tuning the qubit away from the cavity, electromechanical coupling between qubit and mechanical mode can be further enhanced to 40 kHz. In this limit, a small coherent drive of the mechanical resonator results into the splitting of qubit spectrum and we observe interference signature arising from the Landau-Zener-Stuckelberg effect. With further improvements in the qubit coherence, this system offers a novel platform to realize rich interactions and could potentially provide full control over the quantum motional states.