The invention relates to a connector (3) for an infusion bag comprising at least a first tubular body (4) forming an access opening, said tubular body (4) being provided with a bushing (14) having a perforable transverse wall (15) for ensuring the tight closure of the access opening, a perforable stopper (16) arranged hermetically on said transverse wall (15), and a cap (17) for compressing said perforable stopper (16) mounted on said bushing (14) onto the tubular body (4), the surface of said transverse wall (15) which is in contact with the stopper (16) being curved so as to locally increase the compression of said perforable stopper (16) between said cap (17) and said tubular body (4).