Extracting structured knowledge from product profiles is crucial for various applications in e-Commerce. State-of-the-art approaches for knowledge extraction were each designed for a single category of product, and thus do not apply to real-life e-Commerce scenarios, which often contain thousands of diverse categories. This paper proposes TXtract, a taxonomy-aware knowledge extraction model that applies to thousands of product categories organized in a hierarchical taxonomy. Through category conditional self-attention and multi-task learning, our approach is both scalable, as it trains a single model for thousands of categories, and effective, as it extracts category-specific attribute values. Experiments on products from a taxonomy with 4,000 categories show that TXtract outperforms state-of-the-art approaches by up to 10% in F1 and 15% in coverage across all categories.