This paper introduces Continual Learning for Multilingual ASR (CL-MASR), a benchmark for continual learning applied to multilingual ASR. CL-MASR offers a curated selection of medium/low-resource languages, a modular and flexible platform for executing and evaluating various CL methods on top of existing large-scale pretrained multilingual ASR models such as Whisper and AWavLM, and a standardized set of evaluation metrics.