Optically-thin nonlinear polaritonic metasurfaces created by coupling of intersubband nonlinearities in semiconductor heterostructures with optical modes in nanoresonators have recently demonstrated efficient three-wave-mixing at very low pumping intensities of the order of few tens of kW cm-2. In these subwavelength structures, the efficiency and the spectral bandwidth of the wave mixing depends solely on nonlinearity of the constituent meta-atoms. Here we exploit this property to demonstrate an electrically-tunable nonlinear metasurface that combines a plasmonic nanocavity and a quantum-engineered semiconductor heterostructure, in which the magnitude and the spectral characteristics of the nonlinear response are controlled by bias voltage through the quantum-confined Stark effect. We demonstrate tuning the peak second-harmonic-generation (SHG) efficiency in the range of 8.7 – 10.75 μm and modulation of SHG intensity at a fixed pump wavelength by applying bias voltage. An SHG power conversion efficiency of 0.082 % was achieved using a peak pump intensity of only 80 kW cm-2.