Middle English shethe, “close-fitting case or covering for a blade,” from Old English sceaþ, scæþ, from Proto-Germanic *skaith- (source also of Old Saxon scethia, Old Norse skeiðir (plural), Old Frisian skethe, Middle Dutch schede, Dutch schede, Old High German skaida, German scheide “a sheath, scabbard”), perhaps from an extended form of PIE root *skei- “to cut, split,” on the notion of a split stick with the sword blade inserted.

https://www.etymonline.com/word/sheath