The gearbox comprises a case, a stationary rod supported by the case, a gear selector fork mounted slidably on the stationary rod and an end-of-travel bush mounted on the stationary rod so as to provide an axial abutment surface for the gear selector fork. The gear selector fork includes a sheet-metal body forming integrally a pair of support plates each having a respective guide through-hole. One of the guide through-holes is provided with a guide bush formed by means of overmoulding of low-friction plastic and is guided along the stationary rod. The other guide through-hole has no guide bush and is guided along a smaller-diameter portion of the end-of-travel bush.