Abstract : The ANTARES underwater neutrino telescope, located in the Mediterranean Sea at a depth of 2475 m, 40km off the Provencal coast, is composed by an array of 885 photomultipliers distributed on 12 vertical lines. The detector is fully operational since May 2008. Besides the detection of neutrino-induced muons, the telescope is more generally sensitive to particles which emit Cherenkov light, and, thanks to its large volume, offers new opportunities to improve the sensitivity to exotic particles, such as magnetic monopoles. Magnetic monopoles are stable magnetically charged particles first introduced in a consistent manner by Dirac in 1931, which showed that their existence would give an explanation to the quantization of the electric charge. They would have been produced in the Early Universe, and would bring a first proof to the existence of grand unified models. The presentation introduces magnetic monopoles and their signal caracteristics in a neutrino telescope, and then describes the analysis which uses a dedicated algorithm able to reconstruct the velocity of the incoming particles.A new upper limit on the magnetic monopole flux, extracted from ANTARES data taken in 2008, is presented. It is, at present, the best worldwide constraint in the velocity range \beta=[0.65,1[, and provides, for the first time in a neutrino telescope, a constraint for monopole velocities below the Cherenkov threshold.