A medical connector (1) comprising a first rigid body (2) capable of being connected to a medical infusion line and having an elongated tubular element (7) in which there is a conduit (8) opening out at opposite extremities (7A, 7B), a first extremity (7A) of the said tubular element (7) being capable of being directly connected to the medical infusion line, the said elongated tubular element (7) being capable of being closed off at one of its first open extremities by a second body (3) associated with the first body (2). The second body (3) is of yielding material and at least partly covers the elongated element (7) and extends beyond the second extremity (7B) of that element in such a way as to close off the opening thereof, such second body (3) being overmoulded onto the first body (2) and forming a single piece therewith.
