This paper analyzes the compliance of distributed, autonomous block chain management systems (BMS) like Bitcoin—also referred to as ‘virtual currencies’—with the requirements of Islamic Banking and Finance. While intended as a narrow financial and economic analysis, and not as an in-depth analysis of the subtleties and nuances of Shari’a as they relate to banking and finance, it shows that a BMS can conform with the prohibition of riba (usury) and incorporate the principles of maslaha (social benefits of positive externalities) and mutualrisk-sharing (as opposed to risk-shifting). It concludes that Bitcoin or a similar system might be a more appropriate medium of exchange in Islamic Banking and Finance than riba-backed central bank fiat currency, especially among the unbanked and in small-scale cross-border trade.