The appearance of 3D scanners, generating point clouds, has revolutionized anthropometric data collection systems and its applications. Anthropometric data is of paramount importance in several applications, including fashion design, medical diagnosis and virtual character modelling, all of which require an fully-automatic anthropometric measurement extraction method. 3D-based methods for anthropometric measurement extraction become more and more popular due to their improved accuracy compared to classical image-based approaches. Existing 3D methods can be mainly classified in two categories: landmark and template-based methods. The former is highly dependent on the estimated landmarks which is highly sensitive to noise in the input or missing data. The latter has to iteratively solve an objective function to deform a body template to fit the scan, which is time-consuming while being also sensitive to noise and missing data. In this study, we propose the first approach for automatic contact-less Anthropometric Measurements extraction based on Deep-Learning (AM-DL). A novel module dubbed Multi-scale EdgeConv is proposed to learn local features from point clouds at multiple scales. Multi-scale EdgeConv can be directly integrated with other neural networks for various tasks, e.g., classification of point clouds. We exploit this module to design an encoder-decoder architecture which learns to deform a template model to fit a given scan. The measurement values are then calculated on the deformed template model. To evaluate the proposed method, 27 female and 25 male subjects were scanned using a photogrametry-based scanner and measured by an experienced tailor. Experimental results on the synthetic ModelNet40 dataset and on the real scans demonstrate that the proposed method outperforms state-of-the-art methods, and performs sufficiently close to a professional tailor.