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Similarity search based on a distance function in metric spaces is a fundamental problem for many applications. Queries for similar objects lead to the well-known machine learning task of nearest-neighbours identification. Many data indexing strategies, collectively known as Metric Access Methods (MAM), have been proposed to speed up queries for similar elements in this context. Moreover, since exact approaches to solve similarity queries can be complex and time-consuming, alternative options have appeared to reduce query execution time, such as returning approximate results or resorting to distributed computing platforms. In this paper, we introduce MASK (Multilevel Approximate Similarity search with $k$-means), an unconventional application of the $k$-means algorithm as the foundation of a multilevel index structure for approximate similarity search, suitable for metric spaces. We show that inherent properties of $k$-means, like representing high-density data areas with fewer prototypes, can be leveraged for this purpose. An implementation of this new indexing method is evaluated, using a synthetic dataset and a real-world dataset in a high-dimensional and high-sparsity space. Results are promising and underpin the applicability of this novel indexing method in multiple domains.