We report the detection of main-sequence and blue horizontal-branch stars of the Ursa Minor dwarf spheroidal galaxy beyond its tidal radius, indicating the existence of a possible tidal extension in this satellite of the Milky Way. This tidal extension could spread out well beyond the area covered in our survey (R>80'), as suggested by the presence of a ``break'' to a shallower slope observed in its density profile. The V-band surface brightness for this possible tidal extension ranges from 29.8 to 31.5 mag arcsec-2. The area covered in our survey (~1.65 deg2) is not enough to discriminate if this extratidal population is part of a tidal tail or an extended halo around the galaxy. The existence of this tidal extension in Ursa Minor indicates that this satellite is currently undergoing a tidal disruption process by the Milky Way. We discuss the possibility of a tidal origin for the high mass-to-light ratio observed in this galaxy on the basis of our result and recent theoretical simulations of the tidal disruption of dwarf satellites in the Galactic halo.