Waveform physiological data is important in the treatment of critically ill patients in the intensive care unit. Such recordings are susceptible to artefacts, which must be removed before the data can be re-used for alerting or reprocessed for other clinical or research purposes. Accurate removal of artefacts reduces bias and uncertainty in clinical assessment, as well as the false positive rate of intensive care unit alarms, and is therefore a key component in providing optimal clinical care. In this work, we present DeepClean; a prototype self-supervised artefact detection system using a convolutional variational autoencoder deep neural network that avoids costly and painstaking manual annotation, requiring only easily-obtained `good' data for training. For a test case with invasive arterial blood pressure, we demonstrate that our algorithm can detect the presence of an artefact within a 10-second sample of data with sensitivity and specificity around 90%. Furthermore, DeepClean was able to identify regions of artefact within such samples with high accuracy and we show that it significantly outperforms a baseline principle component analysis approach in both signal reconstruction and artefact detection. DeepClean learns a generative model and therefore may also be used for imputation of missing data.