A fluid injection device comprising: - a syringe comprising a body defining a reservoir containing the fluid to be injected, a piston that is arranged to move axially in said body, and a needle provided with an injection tip that is fastened to said body, a second piston being arranged to move axially in the body, said fluid to be injected being arranged between said piston and said second piston, - a piston rod that is axially movable relative to said body and that co-operates with said piston so as to move it axially in said reservoir, - a sleeve that is arranged around said syringe so as to be axially movable relative to said body between a non-projecting position in which said sleeve does not cover said injection tip, and a projecting position in which said sleeve covers said injection tip, said sleeve being in its non-projecting position before the injection device is actuated, and being urged, while in said non-projecting position, towards its projecting position by a compressed spring, the fluid injection device being characterized in that said sleeve comprises an inner portion that extends, at least in part, inside said body, and an outer portion that extends outside said body, said inner portion including at least one radially-deformable tab that, in the non-projecting position of said sleeve, is snap-fastened in at least one respective window of said body, said snap-fastening blocking said sleeve in its non-projecting position, said device including a hollow member co-operating with said second piston, said hollow member being adapted to co-operate after injection, with said at least one radially-deformable tab so as to deform it radially inwards, thereby causing it to cease co-operating with its respective window of said body, so that after said fluid has been injected, said sleeve is moved automatically by said spring towards its projecting position. - a syringe comprising a body defining a reservoir containing the fluid to be injected, a piston that is arranged to move axially in said body, and a needle provided with an injection tip that is fastened to said body, a second piston being arranged to move axially in the body, said fluid to be injected being arranged between said piston and said second piston, - a piston rod that is axially movable relative to said body and that co-operates with said piston so as to move it axially in said reservoir, - a sleeve that is arranged around said syringe so as to be axially movable relative to said body between a non-projecting position in which said sleeve does not cover said injection tip, and a projecting position in which said sleeve covers said injection tip, said sleeve being in its non-projecting position before the injection device is actuated, and being urged, while in said non-projecting position, towards its projecting position by a compressed spring, the fluid injection device being characterized in that said sleeve comprises an inner portion that extends, at least in part, inside said body, and an outer portion that extends outside said body, said inner portion including at least one radially-deformable tab that, in the non-projecting position of said sleeve, is snap-fastened in at least one respective window of said body, said snap-fastening blocking said sleeve in its non-projecting position, said device including a hollow member co-operating with said second piston, said hollow member being adapted to co-operate after injection, with said at least one radially-deformable tab so as to deform it radially inwards, thereby causing it to cease co-operating with its respective window of said body, so that after said fluid has been injected, said sleeve is moved automatically by said spring towards its projecting position.