Ignition coil, and internal combustion engine ignition device

An ignition coil that has a construction allowing direct connection to an ignition plug and that does not need to change the installation space larger when mounted on a cylinder head; and an internal combustion engine ignition device having such ignition coil. The protective outer sleeve (31) of an ignition coil (9) is arranged to be capable of receiving, from the front end (31b) to the inward, the portion of a flange (23) disposed further rearward than its rear end surface (23b) in the main body metal element (19) of an ignition plug (11), and the ignition coil is constructed for direct connection to the ignition plug.