We present the results of deep observations of the Ophiuchus cluster of galaxies with INTEGRAL in the 3-80 keV band. We analyse 3 Ms of INTEGRAL data on the Ophiuchus cluster with the IBIS/ISGRI hard X-ray imager and the JEM-X X-ray monitor. In the X-ray band using JEM-X, we show that the source is extended, and that the morphology is compatible with the results found by previous missions. Above 20 keV, we show that the size of the source is slightly larger than the PSF of the instrument, and is consistent with the soft X-ray morphology found with JEM-X and ASCA. Thanks to the constraints on the temperature provided by JEM-X, we show that the spectrum of the cluster is not well fitted by a single-temperature thermal Bremsstrahlung model, and that another spectral component is needed to explain the high energy data. We detect the high energy tail with a higher detection significance (6.4 sigma) than the BeppoSAX claim (2 sigma). Because of the imaging capabilities of JEM-X and ISGRI, we are able to exclude the possibility that the excess emission comes from very hot regions or absorbed AGN, which proves that the excess emission is indeed of non-thermal origin. Using the available radio data together with the non-thermal hard X-ray flux, we estimate a magnetic field B ~ 0.1-0.2 mu G.