Shroud means the permanent cannot be the target of spells or abilities (CR 702.18a). It is a targeting restriction, nothing more. A spell or ability that says 'target creature' or 'target permanent' cannot legally choose a shroud permanent as its target.
Wrath of God reads 'Destroy all creatures.' The word 'all' means it affects every creature simultaneously without selecting any individual target. Because no targeting is involved, shroud provides zero protection against it (CR 114.1 clarifies that targeting only applies when a spell or ability uses the word 'target').
This is a common misconception: shroud does not grant hexproof, indestructible, or any form of blanket immunity. It exclusively blocks the targeting step of spells and abilities.
Concrete example: Your opponent controls a Morphling (which has shroud). You cast Wrath of God. Morphling is destroyed along with every other creature on the battlefield because Wrath of God does not target — it simply affects all creatures as a non-targeted global effect.
Other global effects that similarly bypass shroud include Cyclonic Rift (overloaded), Damnation, and Day of Judgment — any spell or ability that uses 'each,' 'all,' or 'every' rather than 'target.'
Unofficial fan resource — not affiliated with or endorsed by Wizards of the Coast. Answers are AI-generated estimates grounded in the Comprehensive Rules and are not a substitute for an official judge. Verify anything match-critical.