From the PHB entry for shillelagh:
Components: V, S, M (mistletoe, a shamrock leaf, and a club or quarterstaff)
The wood of a club or quarterstaff you are holding is imbued with nature's power. For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon, and the weapon's damage die becomes a d8. The weapon also becomes magical, if it isn't already. The spell ends if you cast it again or if you let go of the weapon.
It specifically mentions the wooden part, but mechanically makes no mention if it requires it to work. I can see it going either way. Does the weapon need to have a wooden component on it or can it be, for example, 100% glass and metal?