Lexical normalization is the task of transforming an utterance into its standardized form. This task is beneficial for downstream analysis, as it provides a way to harmonize (often spontaneous) linguistic variation. Such variation is typical for social media on which information is shared in a multitude of ways, including diverse languages and code-switching. Since the seminal work of Han and Baldwin (2011) a decade ago, lexical normalization has attracted attention in English and multiple other languages. However, there exists a lack of a common benchmark for comparison of systems across languages with a homogeneous data and evaluation setup. The MultiLexNorm shared task sets out to fill this gap. We provide the largest publicly available multilingual lexical normalization benchmark including 13 language variants. We propose a homogenized evaluation setup with both intrinsic and extrinsic evaluation. As extrinsic evaluation, we use dependency parsing and part-of-speech tagging with adapted evaluation metrics (a-LAS, a-UAS, and a-POS) to account for alignment discrepancies. The shared task hosted at W-NUT 2021 attracted 9 participants and 18 submissions. The results show that neural normalization systems outperform the previous state-of-the-art system by a large margin. Downstream parsing and part-of-speech tagging performance is positively affected but to varying degrees, with improvements of up to 1.72 a-LAS, 0.85 a-UAS, and 1.54 a-POS for the winning system.