This Letter reports on the photometric detection of transits of the Neptune-mass planet orbiting the nearby M-dwarf star GJ 436. It is by far the closest, smallest, and least massive transiting planet detected so far. Its mass is slightly larger than Neptune's at $M = 22.6 \pm 1.9~M_\oplus $. The shape and depth of the transit lightcurves show that it is crossing the host star disc near its limb (impact parameter $0.84 \pm 0.03$) and that the planet size is comparable to that of Uranus and Neptune, $R = 25\,200 \pm 2200$ km = $3.95 \pm 0.35~R_\oplus$. Its main constituant is therefore very likely to be water ice. If the current planet structure models are correct, an outer layer of H/He constituting up to ten percent in mass is probably needed on top of the ice to account for the observed radius.