Automatic decision and prediction systems are increasingly deployed in applications where they significantly impact the livelihood of people, such as for predicting the creditworthiness of loan applicants or the recidivism risk of defendants. These applications have given rise to a new class of algorithmic-fairness specifications that require the systems to decide and predict without bias against social groups. Verifying these specifications statically is often out of reach for realistic systems, since the systems may, e.g., employ complex learning components, and reason over a large input space. In this paper, we therefore propose stream-based monitoring as a solution for verifying the algorithmic fairness of decision and prediction systems at runtime. Concretely, we present a principled way to formalize algorithmic fairness over temporal data streams in the specification language RTLola and demonstrate the efficacy of this approach on a number of benchmarks. Besides synthetic scenarios that particularly highlight its efficiency on streams with a scaling amount of data, we notably evaluate the monitor on real-world data from the recidivism prediction tool COMPAS.