We report on INTEGRAL observations of the soft $gamma$-ray repeater SGR 1935+2154 performed between 2020 April 28 and May 3. Several short bursts with fluence of $sim10^{-7}-10^{-6}$ erg cm$^{-2}$ were detected by the IBIS instrument in the 20-200 keV range. The burst with the hardest spectrum, discovered and localized in real time by the INTEGRAL Burst Alert System, was spatially and temporally coincident with a short and very bright radio burst detected by the CHIME and STARE2 radio telescopes at 400-800 MHz and 1.4 GHz, respectively. Its lightcurve shows three narrow peaks separated by $sim$29 ms time intervals, superimposed on a broad pulse lasting $sim$0.6 s. The brightest peak had a delay of 6.5$pm$1.0 ms with respect to the 1.4 GHz radio pulse (that coincides with the second and brightest component seen at lower frequencies). The burst spectrum, an exponentially cut-off power law with photon index $Gamma=0.7_{-0.2}^{+0.4}$ and peak energy $E_p=65pm5$ keV, is harder than those of the bursts usually observed from this and other magnetars. By the analysis of an expanding dust scattering ring seen in X-rays with the {it Neil Gehrels Swift Observatory} XRT instrument, we derived a distance of 4.4$_{-1.3}^{+2.8}$ kpc for SGR 1935+2154, independent of its possible association with the supernova remnant G57.2+0.8. At this distance, the burst 20-200 keV fluence of $(6.1pm 0.3)times10^{-7}$ erg cm$^{-2}$ corresponds to an isotropic emitted energy of $sim1.4times10^{39}$ erg. This is the first burst with a radio counterpart observed from a soft $gamma$-ray repeater and it strongly supports models based on magnetars that have been proposed for extragalactic fast radio bursts.
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