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