Compact laser sources operating in mid infrared spectral region with stable emission are important for applications in spectroscopy and wireless communication. Quantum cascade lasers (QCL) are unique semiconductor sources covering mid infrared frequency range. Based on intersubband transitions, the carrier lifetime of these sources is in the ps range. For this reason their frequency response to direct modulation is expected to overcome the limits of standard semiconductor lasers. In this work injection locking of the roundtrip frequency of a QCL emitting at 9 μm is reported. Inter modes laser frequency separation is stabilized and controlled by an external microwave source. Designing an optical waveguide embedded in a microstrip line a flat frequency response to direct modulation up to 14 GHz is presented. Injection locking over MHz frequency range at 13.7 GHz is demonstrated. Numerical solutions of injection locking theory are discussed and presented as tool to describe experimental results.