Using 2.5 Ms of data obtained by the INTEGRAL  satellite in 2003-2004, we discovered persistent hard X-ray emission from the soft gamma-ray repeater SGR 1900+14. Its 20-100 keV spectrum is well described by a steep power law with photon index $\Gamma=3.1\pm0.5$ and flux $1.5\times10^{-11}$ erg cm-2 s-1. Contrary to SGR 1806–20, the only other soft gamma-ray repeater for which persistent emission above 20 keV was reported, SGR 1900+14 has been detected in the hard X-ray range while it was in a quiescent state (the last bursts from this source were observed in 2002). By comparing the broad band spectra (1-100 keV) of all the magnetars detected by INTEGRAL  (the two SGRs and three anomalous X-ray pulsars) we find evidence for a different spectral behaviour of these two classes of sources.