Magnetars are isolated neutron stars powered by magnetic energy. They are often observed as Soft Gamma- ray Repeaters (SGRs), i.e. sources of short, repeating bursts of hard X-rays. Fast radio bursts (FRBs) consist of bright ms-long pulses of radio emission, with no counterparts at other wavelengths. A few of them have been associated with galaxies at redshifts z=0.03-0.7. This suggests an extragalactic origin for the whole class, but the true nature of FRBs is still an unsolved mystery. On 2020 April 28, the INTEGRAL Burst Alert System localized with arcmin precision a hard X-ray burst from the well known Galactic magnetar SGR 1935+2154. This burst was also seen as an extremely bright, short radio pulse by the CHIME and STARE2 radio telescopes. This first association between an FRB-like radio pulse and a high-energy burst from a SGR is an important advance for our understanding of FRBs, providing strong support to models based on magnetars.