A closure capsule for closing a container, comprising: —a cap (2) to be associated with a container and comprising a frangible mouth (20); —a cutter (3) comprising a cutting edge (30) designed to open said frangible mouth (20); at least the cap (2) and the cutter (3) in combination defining a reservoir (8) for containing a substance to be dropped into the container when the frangible mouth (20) is opened; —a protective covering (4) for the cap (2) and the cutter (3), separate from the cutter (3) and, in turn, comprising: i) a lateral wall (40) that encloses a zone (402) for at least partially housing the cutter (3); ii) a base (41) from which said lateral wall (40) extends; —transmitting means (5) for transmitting an opening torque, from the covering to the cutter, for opening the frangible mouth (20), said transmitting means (5) comprising a first and a second portion (51, 52) incorporated in the covering (4) and in the cutter (3), respectively; said first portion (51) being incorporated in the base (41).