The Player's Handbook describes the shield as being wielded in one hand.
However, the Armor category that displays the times to put on armor lists the shield is something that you don, and it takes one action to do so. Under this interpretation, can you even be disarmed of your shield, very much the way you cannot be disarmed of your armor?
We have, effectively, three points of information. First,
the entry on the disarm variant rule states that
A creature can use a weapon attack to knock a weapon or another item from a target's grasp.
and the entry on the battlemaster’s disarming attack lets you
When you hit a creature with a weapon attack, you can [...force...] it to drop one item of your choice that it's holding.
So the question becomes whether or not a shield is an item that you “hold” or is in your “grasp.” To answer that, we have two more points to consider:
The entry on shields says
A shield [...] is carried in one hand.
While weapons don’t usually require an action to draw, as the Use an Object action states that
You normally interact with an object while doing something else, such as when you draw a sword as part of an attack.
shields instead require their own separate action to “don,” as indicated by the “donning and doffing armor” table on page 146.
These last two imply but do not state completely opposite answers to the question of whether or not a shield is a held item that can be disarmed. Neither one of them explicitly or conclusively says one way or the other, but “carried in one hand” suggests that the shield is merely held, while “donning” and taking extra time to do so implies that the shield is strapped on.
We do not have enough information to definitively state an answer one way or the other.
Yes, shields can be disarmed. There are only two methods of disarming in the game at present - the variant rule in the DMG, and the Battlemaster Fighter's Disarming Attack. Both of these can disarm someone of a shield. The variant rule in the DMG says:
Disarm
A creature can use a weapon attack to knock a weapon or another item from a target's grasp. The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.
The attacker has disadvantage on its attack roll if the target is holding the item with two or more hands. The target has advantage on its ability check if it is larger than the attacking creature, or disadvantage if it is smaller.
This allows you to disarm someone of any "item" they have in their grasp. I should emphasize, though, that this is a variant rule from the DMG, and as such is only included if the DM specifically chooses to allow it.
For reference, the entry on shields says:
A shield is made from wood or metal and is carried in one hand.
Shields are definitely "items", and carrying something in one hand is synonymous with having it in your grasp, so yes, shields can be disarmed this way. As for the Battlemaster Fighter's Disarming Attack, it says:
Disarming Attack. When you hit a creature with a weapon attack, you can expend one superiority die to attempt to disarm the target, forcing it to drop one item of your choice that it's holding. You add the superiority die to the attack's damage roll, and the target must make a Strength saving throw. On a failed save, it drops the object you choose. The object lands at its feet.
This allows you to disarm a target of an item that it's holding. Holding is again synonymous with carrying in one hand, so this, too, can disarm someone of a shield.
I thought I might chime in as I actually use a shield IRL. I would like to point out that a person can be disarmed of their shield while still wearing it.
A shield as stated above is strapped to a person's arm and held by a handle to stabilize it and keep it from flopping about uselessly. This is how you disarm someone: you get them to release the handle through pain or breakage, and it flops around, sliding down the arm (note the shape of your arm), and becomes a hindrance to regrab or drop as it never comes off quickly. This, in effect, disarms the shield.
That being said, it is very difficult to disarm a person of their shield, as their hand is, well, behind a shield.
The Sage Advice Compendium v. 2.5 says:
[NEW] Can the Disarming Attack maneuver disarm a creature of a shield it has donned?
No. Disarming Attack forces a creature to drop an object it is holding. Donned shields aren’t merely held.
I think it can be disarmed. Disarm doesn't mean flipping with a sword or something. There could be more than one ways to "Disarm" a weapon or shield.
Some explained here, that shield can be donned by strapping it to your arm. Well, then you can disarm it by cutting the straps with your weapon, for example.
Or when you think about it, you could overpower your opponent and just get it from his hands.. etc..
