The rules on deflecting are as follows for 3rd level Monks (PHB, p. 78, bold added):
You can use your reaction to deflect or catch the missile when you are
hit by a ranged weapon attack. When you do so, the damage you take
from the attack is reduced by 1d10 + your Dexterity modifier + your
If you reduce the damage to 0, you can catch the missile if it is
small enough for you to hold in one hand and you have at least one
hand free. If you catch a missile in this way, you can spend 1 ki
point to make a ranged attack with the weapon or piece of ammunition
you just caught, as part of the same reaction.
A net counts as a ranged weapon, and requires an attack roll to hit (so far so good), but it's unclear to me whether or not it counts as a "missile" since it isn't thrown with the intent of transferring kinetic energy to a target. Similarly, I considered it less than obvious whether you could be said to "reduce the damage to 0" when the net's initial attack never did any damage in the first place.
So I'm throwing this question to the stack. Is an attack with a net an attack which a monk could "deflect", in the sense of catching it and throwing it back at an enemy (with a reaction and a ki point)?
Usually a net that can restrain you is not small enough to hold in one hand. It might be able to be held in one hand, but not when it is thrown against you. This requires a DM ruling that makes sense, though.
You do not reduce the damage to 0, because there is no damage to reduce*. You don't roll any damage for net. This is different with a dart thrown by someone with -1 dexterity modifier and with damage roll of 1. The damage is 0, but there is damage to reduce, so you can still catch it.