So, one of my players was going for a Diestro style fighting and took the "Disarm" action. I thought "that's cool," but then he used it in combat and asked: "So, What happens?"

…

I didn't really know how to rule it. The action card has a 5 recharge so I assume that it should have SOME kind of penalty. I first thought that they would need to use a maneuver to pick it up, but then that seemed too weak. I thought maybe the NPC should be without weapon damage for "some time" but I settled on just saying the NPC could either attack with no weapon damage or use an action to retrieve/pull out another weapon.

Has anyone else run into this?

Technically, the NPC loses their weapon and must spend a maneuver to pick it up. This means they cannot PARRY until their turn. As a GM, you could also rule that to pick up the fallen weapon is an ACTION (perform a stunt) while engaged with an enemy.  This would then make it useful simply to prevent an attack the enemy's next round.  

Lastly, your player *could* consider doing a disarm action, and then a maneuver to pick up the enemy's weapon (or perhaps kick it away, etc) before the enemy has a chance to get it back.