Many industrial applications use Metric Learning as a way to circumvent scalability issues when designing systems with a high number of classes. Because of this, this field of research is attracting a lot of interest from the academic and non-academic communities. Such industrial applications require large-scale datasets, which are usually generated with web data and, as a result, often contain a high number of noisy labels. While Metric Learning systems are sensitive to noisy labels, this is usually not tackled in the literature, that relies on manually annotated datasets. In this work, we propose a Metric Learning method that is able to overcome the presence of noisy labels using our novel Smooth Proxy-Anchor Loss. We also present an architecture that uses the aforementioned loss with a two-phase learning procedure. First, we train a confidence module that computes sample class confidences. Second, these confidences are used to weight the influence of each sample for the training of the embeddings. This results in a system that is able to provide robust sample embeddings. We compare the performance of the described method with current state-of-the-art Metric Learning losses (proxy-based and pair-based), when trained with a dataset containing noisy labels. The results showcase an improvement of 2.63 and 3.29 in Recall@1 with respect to MultiSimilarity and Proxy-Anchor Loss respectively, proving that our method outperforms the state-of-the-art of Metric Learning in noisy labeling conditions.