The invention relates to an injection unit (13) for a machine for making containers via blow molding or stretch blow molding, in a mold (8) cavity having the shape of the containers (2), using plastic blanks (3), wherein said injection unit (13) comprises: a plasticizer unit (14) defining a fluid pipe and provided with at least one fluid supply port (18) in communication with the fluid pipe, a movable element (24) provided with a bell nozzle (25) in fluid communication with the pipe, the movable element (24) being slidably mounted relative to the plasticizer unit (14); a system (46) for magnetically attaching the movable element (24) to the plasticizer unit (14) that is capable of retaining the movable element (24), under the weight thereof, in a safety position in which the bell nozzle (25) is spaced apart from the mold.