The disclosure relates to a connector for packaging containing medical fluids, in particular infusion or transfusion bags, including a tubular connection part for receiving a spike for the withdrawal of fluid, and having a lower opening on the packaging side and an upper opening on the connection side. A self-sealing membrane, which is pierced by the spike, is located in the connection part. The membrane has an upper, annular section leading into a lower, plate-shaped section, said annular section of the membrane surrounding the spike in a sealing manner, when the latter pierces the plate-shaped section. The membrane acts as a guide for the spike and also reseals the connector, once the spike has been removed.