Missing data is a recurrent and challenging problem, especially when using machine learning algorithms for real-world applications. For this reason, missing data imputation has become an active research area, in which recent deep learning approaches have achieved state-of-the-art results. We propose DAEMA (Denoising Autoencoder with Mask Attention), an algorithm based on a denoising autoencoder architecture with an attention mechanism. While most imputation algorithms use incomplete inputs as they would use complete data - up to basic preprocessing (e.g. mean imputation) - DAEMA leverages a mask-based attention mechanism to focus on the observed values of its inputs. We evaluate DAEMA both in terms of reconstruction capabilities and downstream prediction and show that it achieves superior performance to state-of-the-art algorithms on several publicly available real-world datasets under various missingness settings.