A rate equation analysis on the modulation response of an optical injection-locked quantum cascade laser is outlined. It is found that the bifurcation diagram exhibits both bistable and unstable locked regions. In addition, the stable locked regime widens as the linewidth enhancement factor increases. It is also shown that both positive and negative optical detunings as well as strong injection strength enhance the 3 dB modulation bandwidth by as much as 30 GHz. Finally, the peak in the modulation response is significantly influenced by the optical frequency detuning.