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. <EOS>