Phase modulation is demonstrated in a quantum Stark effect modulator designed to operate in the mid-infrared at wavelength around 10 µm. Both phase and amplitude modulation are simultaneously resolved through the measurement of the heterodyne signal arising from the beating of a quantum cascade laser with a highly stabilized frequency comb. The highest measured phase shift is more than 5 degrees with an associated intensity modulation of 5 %. The experimental results are in full agreement with our model in which the complex susceptibility is precisely described considering the linear voltage dependent Stark shift of the optical resonance.