The modulation properties of optical injection-locked quantum cascade lasers (QCLs) are investigated theoretically via a simple low dimensional rate equation model. It is found that both strong injection level and positive optical frequency detuning increase the modulation bandwidth, while a large linewidth enhancement factor (LEF) contributes to the enhancement of the peak magnitude in the intensity modulation (IM) response. As opposed to conventional injection-locked interband lasers, it is demonstrated that no dip occurs in the QCL's IM response, which is beneficial for a series of broadband microwave photonic applications. Computations also show that the value of the LEF can critically modify both the locking and stability regions on the optical frequency detuning injection level map.