High-power, high-speed quantum cascade lasers (QCLs) with stable emission in the mid-infrared regime are of great importance for applications in metrology, telecommunication, and fundamental tests of physics. Owing to the intersubband transition, the unique ultrafast gain recovery time of the QCL with picosecond dynamics is expected to overcome the modulation limit of classical semiconductor lasers and bring a revolution for the next generation of ultrahigh-speed optical communication. Therefore, harmonic injection locking, offering the possibility to fast modulate and greatly stabilize the laser emission beyond the rate limited by cavity length, is inherently adapted to QCLs. In this work, we demonstrate for the first time the harmonic injection locking of a mid-infrared QCL with an output power over 1 W in continuous-wave operation at 288 K. Compared with an unlocked laser, the intermode spacing fluctuation of an injection-locked QCL can be considerably reduced by a factor above $1\times {10}^3$, which permits the realization of an ultrastable mid-infrared semiconductor laser with high phase coherence and frequency purity. Despite temperature change, this fluctuation can be still stabilized to hertz level by a microwave modulation up to $～18\mathrm{GHz}$. These results open up the prospect of the applications of mid-infrared QCL technology for frequency comb engineering, metrology, and the next-generation ultrahigh-speed telecommunication. It may also stimulate new schemes for exploring ultrafast mid-infrared pulse generation in QCLs.