Operation of continuous wave quantum cascade lasers with a frequency-shifted feedback provided by an acousto-optic modulator is reported. Measured linewidth of 1.7 cm−1 for these devices, under CW operating conditions, was in a good agreement with predictions of a model based on frequency-shifted feedback seeded by spontaneous emission. Linewidth broadening was observed for short sweep times, consistent with sound wave grating period variation across the illuminated area on the acousto-optic modulator. Standoff detection capability of the AOM-based QCL setup was demonstrated for several solid materials.