WASHINGTON—The Supreme Court ruled unanimously Wednesday that states may not impose excessive fines, extending a bedrock constitutional protection but potentially jeopardizing asset-forfeiture programs that help fund police operations with property seized from criminal suspects.

“For good reason, the protection against excessive fines has been a constant shield throughout Anglo-American history: Exorbitant tolls undermine other constitutional liberties,” Justice Ruth Bader Ginsburg wrote for the court, warning that tyrants...