Multilingual biomedical entity linking (MBEL) aims to map language-specific mentions in the biomedical text to standardized concepts in a multilingual knowledge base (KB) such as Unified Medical Language System (UMLS). In this paper, we propose Con2GEN, a prompt-based controllable contrastive generation framework for MBEL, which summarizes multidimensional information of the UMLS concept mentioned in biomedical text into a natural sentence following a predefined template. Instead of tackling the MBEL problem with a discriminative classifier, we formulate it as a sequence-to-sequence generation task, which better exploits the shared dependencies between source mentions and target entities. Moreover, Con2GEN matches against UMLS concepts in as many languages and types as possible, hence facilitating cross-information disambiguation. Extensive experiments show that our model achieves promising performance improvements compared with several state-of-the-art techniques on the XL-BEL and the Mantra GSC datasets spanning 12 typologically diverse languages.