A closure (1) for a medicament bottle has a cap portion (2), which can be joined to the bottle and which has at least one opening (3) closed by an elastic, puncturable sealing layer (4). The opening (3) is covered on the exterior of the cap portion by a cover element (5) which, with its edge area (6) that encircles the opening (3), is joined with positive, interlocking fit, but without material bonding with the rim (8) of the opening (3). The sealing layer touches the rear side of the covering element facing the opening in a manner that is flush, sterile and without material bonding. The closure is made by a process in which the cap portion and cover element(s) are first produced and joined together, and then the sealing layer is injected into the cap portion.