We present a compact nonlinear compression scheme for the generation of millijoule few-cycle pulses beyond 4 µm wavelength. For this purpose 95 fs pulses at 5 µm from a 1 kHz midwave-IR optical parametric chirped pulse amplifier (OPCPA) are spectrally broadened due to a self-phase modulation in ZnSe. The subsequent compression in a bulk material yields 53 fs pulses with 1.9 mJ energy. The compression succeeds efficiently with only slight beam distortions and an energy throughput of 85%, which results in a peak power of 34 GW. The nonlinear refractive index of ZnSe was derived from the nonlinear compression and self-focusing measurements. Furthermore, we explore to which extent multiphoton absorption affects the nonlinear compression regime.