Anti-money laundering and countering the financing of terrorism (AML) laws require banks to deploy transaction monitoring systems (TMSs) to detect suspicious activity of bank customers and report the activity to law enforcement authorities. Because the monitoring of customer data to detect suspicious activity interferes with fundamental rights, AML systems must comply with the proportionality test under European fundamental rights law, as most recently expressed by the Court of Justice of the European Union (CJEU) in the Digital Rights Ireland and Tele2 Sverige-Watson cases. To our knowledge there has been no analysis as to whether AML systems are compliant with the proportionality test as expressed in these latest cases. Understanding how the proportionality test applies to current AML systems is all the more important as banks and regulators consider moving to AI-based tools to detect suspicious transactions. The objective of this paper is twofold: to study whether current AML systems are compliant with the proportionality test, and to study whether a move toward AI in AML systems could exacerbate the proportionality problems. Where possible, we suggest possible cures to the proportionality problems identified.