An essential part of the financial system is its infrastructure: for example, payment systems, securities settlement systems, central counterparties and messaging services. These enable transactions ranging from retail payments through to business in domestic and international wholesale financial markets. Given this, were any such system to fail, this could affect the whole economy. This threat to financial stability largely explains why central banks seek to ensure - via their "oversight" role - that financial infrastructures take sufficient measures to mitigate risk. This paper explores the role of governance of infrastructures in the management of systemic risk. We do this by considering the case of a generic infrastructure provider operating under different forms of ownership. We show that, in the presence of consumption externalities, the level of risk mitigation chosen by the infrastructure provider is less than socially optimal. We then show that governance may have a role in adapting a provider's decision-making process to take due account of their risk externalities and, hence, provide a more socially optimal level of risk mitigation. Specifically, we suggest a feasible adaptation could be for infrastructures to appoint external stakeholder representatives to their boards with a specific remit to act in the wider public interest.