Yes, it can.
In a nutshell, Protection from X on a creature means:
- The creature can't be targeted by X spells or abilities from source with X.
- It can't be blocked by X creatures.
- Damage from X sources is prevented.
- Auras with quality X on that creature are destroyed, equipments with quality X fall off (but are not destroyed).
Day of Judgment or similar cards do not target any creatures, and they deal no damage. Therefore, Protection would not protect that creature.
Reference:
702.15. Protection
702.15a Protection is a static ability, written "Protection from [quality]." This quality is usually a color (as in "protection from black") but can be any characteristic value. If the quality happens to be a card name, it is treated as such only if the protection ability specifies that the quality is a name. If the quality is a card type, subtype, or supertype, the ability applies to sources that are permanents with that card type, subtype, or supertype and to any sources not on the battlefield that are of that card type, subtype, or supertype. This is an exception to rule 109.2.
702.15b A permanent or player with protection can't be targeted by spells with the stated quality and can't be targeted by abilities from a source with the stated quality.
702.15c A permanent or player with protection can't be enchanted by Auras that have the stated quality. Such Auras attached to the permanent or player with protection will be put into their owners' graveyards as a state-based action. (See rule 704, "State-Based Actions.")
702.15d A permanent with protection can't be equipped by Equipment that have the stated quality or fortified by Fortifications that have the stated quality. Such Equipment or Fortifications become unattached from that permanent as a state-based action, but remain on the battlefield. (See rule 704, "State-Based Actions.")
702.15e Any damage that would be dealt by sources that have the stated quality to a permanent or player with protection is prevented.
702.15f Attacking creatures with protection can't be blocked by creatures that have the stated quality.
702.15g "Protection from [quality A] and from [quality B]" is shorthand for "protection from [quality A]" and "protection from [quality B]"; it behaves as two separate protection abilities. If an effect causes an object with such an ability to lose protection from [quality A], for example, that object would still have protection from [quality B].
702.15h "Protection from all [characteristic]" is shorthand for "protection from [quality A]," "protection from [quality B]," and so on for each possible quality the listed characteristic could have; it behaves as multiple separate protection abilities. If an effect causes an object with such an ability to lose protection from [quality A], for example, that object would still have protection from [quality B], [quality C], and so on.
702.15i "Protection from everything" is a variant of the protection ability. A permanent with protection from everything has protection from each object regardless of that object's characteristic values. Such a permanent can't be targeted by spells or abilities, enchanted by Auras, equipped by Equipment, fortified by Fortifications, or blocked by creatures, and all damage that would be dealt to it is prevented.
702.15j Multiple instances of protection from the same quality on the same permanent or player are redundant.