"A shield is made from wood or metal and is carried in one hand. Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time." ~quoted from the rules (and the D&D Beyond site).
Edit for the link: Shield
In that description, it's not even said to be armor. It's a hand-item which can be wielded to gain the benefit of +2 AC.
For comparison the definition of half-plate is: "Half-plate consists of shaped metal plates that cover most of the wearers body. It does not include leg protection beyond simple greaves that are attached with leather straps."
So I guess half-plate is not armor either since it is "not even said to be armor"
A shield is listed on page 146 as requiring an action to doff AND it also defined doff as taking it off.
A shield is in the table labeled "Donning and Doffing Armor" also on page 146 and is in the table labeled "ARMOR" on page 145.