This work theoretically investigates the frequency noise (FN) characteristics of quantum cascade lasers subject to the optical injection through a set of coupled rate equations with Langevin noise sources. It is shown that the low-frequency FN is completely suppressed by the optical injection, and the suppression bandwidth increases with the increasing injection ratio. The optimal FN peak suppression ratio at an injection ratio of 10 dB reaches 2.9 dB. In addition, it is found that the optical

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... njection at positive frequency detunings close to the locking boundary invokes an additional peak in the FN spectrum, which can be higher than the carrier noise-induced one of free-running lasers. This peak amplitude strongly depends on the value of the linewidth broadening factor. Unlike injection-locked interband lasers, the FN peak does not necessarily exhibit a resonance.