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:
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.