We present the power spectrum of galaxy clusters measured from the new ROSAT‐ESO Flux‐Limited X‐Ray (REFLEX II) galaxy cluster catalogue. This new sample extends the flux limit of the original REFLEX catalogue to 1.8 × 10−12 erg s−1 cm−2, yielding a total of 911 clusters with ≥94 per cent completeness in redshift follow‐up. The analysis of the data is improved by creating a set of 100 REFLEX II‐catalogue‐like mock galaxy cluster catalogues built from a suite of large‐volume Λ cold dark matter (ΛCDM) N‐body simulations (L‐BASICC II). The measured power spectrum is in agreement with the predictions from a ΛCDM cosmological model. The measurements show the expected increase in the amplitude of the power spectrum with increasing X‐ray luminosity. On large scales, we show that the shape of the measured power spectrum is compatible with a scale‐independent bias and provide a model for the amplitude that allows us to connect our measurements with a cosmological model. By implementing a luminosity‐dependent power‐spectrum estimator, we observe that the power spectrum measured from the REFLEX II sample is weakly affected by flux‐selection effects. The shape of the measured power spectrum is compatible with a featureless power spectrum on scales k > 0.01 h Mpc−1 and hence no statistically significant signal of baryonic acoustic oscillations can be detected. We show that the measured REFLEX II power spectrum displays signatures of non‐linear evolution.