A debate has recently emerged in Heterodox Economics and Political Economy on the nature of monetary sovereignty, and whether it can be democratised and wielded to address the social and environmental catastrophes of our age. While Modern Monetary Theory understands monetary sovereignty to be relatively unconstrained, post-Keynesian, Structuralist and Critical Macro-Finance approaches point to various external limits on states’ abilities to govern money – from the international currency hierarchy to the offshore nature of money creation. This article evaluates this debate in light of Marx’s monetary theory. Under capitalism, money constitutes the social adhesive of a world of privatised production and mass dispossession, which conjures an anonymous, competitive logic that Marx terms the ‘law of value’. To function in this way, money must be underpinned by an historically novel form of state sovereignty. The state must both back money with its coercive powers and insulate monetary governance from popular forces, or else risk losing the confidence of the profit-driven private actors upon which money relies. Yet in exercising its sovereign capacity to govern domestic and international money relations, the state inadvertently reproduces the law of value on a global scale – an ‘Invisible Leviathan’ that subordinates states to its dictates. Contra the Heterodox literature, then, monetary sovereignty is not a vehicle for radical democracy or social/environmental justice, nor is it simply constrained by external limits. Instead, monetary sovereignty is innately a practice of depoliticisation that unwittingly produces a global logic of economic domination that binds states’ hands.