I attacked a deer with one of my hunting parties early game, and the unit just became invisible. I could still select it, but I could not see it anymore. 

My hunting party disappeared after being attacked by other civ. And I could escape and walking as invisible unit.

I had the same issue, in my most recent game and about 10-20 turns later the issue was resolved. However, later game got hard stuck on turn 130 and wouldnt let me go into the next turn, have to start a new game and see if it occurs again.

I encountered the same issue:
Stationed Hunting party
Attacked deer

Became Invisible

Another same issue here. Hunting party was invisible after attacking a deer

I've noticed that also an enemy hunting party was also invisible and that a preview for a battle was stuck and wouldn't go away. However, after opening another battle preview with my invisible hunting party (and the enemy's invisible hunting party as well) both units became visible again. You don't have to go into any battles, just preview them.