Regeneration only replaces destruction. According to CR 701.15a, to sacrifice a permanent means to move it from the battlefield to its owner's graveyard as a cost or effect — this is not the same as the creature being destroyed. Regeneration only replaces a destruction event (CR 701.13), so it has no interaction with sacrifice whatsoever.
CR 614.1 explains that replacement effects (including regeneration shields) modify specific events. Since sacrifice is not a destruction event, no regeneration shield is triggered or consumed when a creature is sacrificed.
This is why effects that say "sacrifice a creature" are often used deliberately to get around indestructible and regeneration alike — both of those abilities only protect against destruction, not sacrifice.
Concrete example: Your opponent controls a Darksteel Colossus with a regeneration shield on it (somehow applied). You cast Innocent Blood, forcing them to sacrifice a creature. They must sacrifice the Colossus; the regeneration shield does nothing to prevent this, and the Colossus goes to the graveyard.
Bottom line: if you need to remove a creature that can regenerate, forcing its controller to sacrifice it (e.g., via Diabolic Edict or Geth's Verdict) completely bypasses regeneration.
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.