We report the discovery of a high-energy transient with the IBIS/ISGRI detector on board the INTEGRAL observatory. The source, namely IGR J00291+5934, was first detected on 2nd December 2004 in the routine monitoring of the IBIS/ISGRI 20--60 keV images. The observations were conducted during Galactic Plane Scans, which are a key part of the INTEGRAL Core Programme observations. After verifying the basic source behaviour, the discovery was announced on 3rd December. The transient shows a hard Comptonised spectrum, with peak energy release at about 20 keV and a total luminosity of ~ 0.9E36 erg/s in the 5--100 keV range, assuming a distance of 3 kpc. Following the INTEGRAL announcement of the discovery of IGR J00291+5934, a number of observations were made by other instruments. We summarise the results of those observations and, together with the INTEGRAL data, identifiy IGR J00291+5934 as the 6th member of a class of accreting X-ray millisecond pulsars.