We report the discovery of X-ray pulsations at 105.2 Hz (9.5 ms) from the transient X-ray binary IGR J16597–3704 using NuSTAR and Swift. The source was discovered by INTEGRAL in the globular cluster NGC 6256 at a distance of 9.1 kpc. The X-ray pulsations show a clear Doppler modulation that implies an orbital period of ~46 min and a projected semi-major axis of ~5 lt-ms, which makes IGR J16597–3704 an ultracompact X-ray binary system. We estimated a minimum companion mass of 6.5 × 10−10 M⊙, assuming a neutron star mass of 1.4 M⊙, and an inclination angle of <75° (suggested by the absence of eclipses or dips in its light curve). The broad-band energy spectrum of the source is well described by a disk blackbody component (kT ~ 1.4 keV) plus a comptonised power-law with photon index ~2.3 and an electron temperature of ~30 keV. Radio pulsations from the source were unsuccessfully searched for with the Parkes Observatory.