We exploited the high sensitivity of the INTEGRAL IBIS/ISGRI instrument to study the persistent hard X-ray emission of the soft gamma-ray repeater SGR 1900+14, based on ~11.6 Ms of archival data. The 22-150 keV INTEGRAL spectrum can be well fit by a power law with photon index 1.9 +/- 0.3 and flux F_x = (1.11 +/- 0.17)E-11 erg/cm^2/s (20-100 keV). A comparison with the 20-100 keV flux measured in 1997 with BeppoSAX, and possibly associated with SGR 1900+14, shows a luminosity decrease by a factor of ~5. The slope of the power law above 20 keV is consistent within the uncertainties with that of SGR 1806-20, the other persistent soft gamma-ray repeater for which a hard X-ray emission extending up to 150 keV has been reported.