We present new Suzaku and Fermi data and re-analysed archival hard X-ray data from the INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) and Swift–Burst Alert Telescope (BAT) surveys to investigate the physical properties of the luminous, high-redshift, hard X-ray-selected blazar IGR J22517+2217, through the modelling of its broad-band spectral energy distribution (SED) in two different activity states. Through analysis of new Suzaku data and flux-selected data from archival hard X-ray observations, we build the source SED in two different states, one for the newly discovered flare that occurred in 2005 and one for the following quiescent period. Both SEDs are strongly dominated by the high-energy hump peaked at 1020–1022 Hz, which is at least two orders of magnitude higher than the low-energy (synchrotron) one at 1011–1014 Hz and varies by a factor of 10 between the two states. In both states the high-energy hump is modelled as inverse Compton emission between relativistic electrons and seed photons produced externally to the jet, while the synchrotron self-Compton component is found to be negligible. In our model the observed variability can be accounted for by a variation of the total number of emitting electrons and by a dissipation region radius changing from inside to outside the broad-line region as the luminosity increases. In its flaring activity, IGR J22517+2217 is revealed as one of the most powerful jets among the population of extreme, hard X-ray-selected, high-redshift blazars observed so far.