A pre-filled hypodermic syringe includes a tubular body having two open ends and containing a fluid to be administered to a patient; a plunger which, having at one of its ends a piston mounted to slide in the tubular body, passes through the opening of the first end of the tubular body; a tip for connection in the form of a cone of the Luer or Luer-Lock type, for example for connecting to a needle or to a drip, intended to pass the fluid that is to be administered and comprising a tubular part communicating with the opening of the second end; the tip comprising an obturator connected by a frangible region to the free end of its tubular part, the syringe being made of a synthetic material and obtained by molding, the obturator being molded as one piece with the tip and the tubular body.