Yes you could dispel it, but the initial attack would still miss
The DMG has guidance on when Readied actions (and reactions and triggers in general) occur:
follow whatever timing is specified in the reaction's description. For example, the opportunity attack and the shield spell are clear about the fact that they can interrupt their triggers. If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action. (DMG p. 252, bold added)
Your dispel magic spell could certainly remove the shield spell from a target (so they wouldn't have a +5 to AC for the rest of the round): but it could only do so after the shield spell had been successfully cast. And the casting of the shield spell will disrupt the initial attack which triggered it.
If you want to stop the Shield spell from taking effect at all, use counterspell, not dispel magic, as suggested in the Sage Advice Compendium, p. 15 (which also wouldn't require you to Ready a spell, spending both an action and a spell slot before you're sure your enemy even intends to cast a spell).