You touch a willing creature who isn't wearing armor, and a protective
magical force surrounds it until the spell ends. The target's base AC
becomes 13 + its Dexterity modifier. The spell ends if the target dons
armor or if you dismiss the spell as an action.
A shield grants a +2 bonus to AC, and is in the list of equipment that can be donned and doffed. Can the spell be cast on someone wielding a shield, and would it end if cast on a person who then dons a shield?
As a sidenote, while this question shares similarities with a previously asked question (Does Mage Armor stack with Shield?), that question deals primarily with whether untyped bonuses can add onto mage armor, and whether the two spell effects can combine, whereas this question queries a specific limitation of the mage armor spell (cannot work with armour) and whether a shield counts as armour in this regard.