Depression detection research has increased over the last few decades, one major bottleneck of which is the limited data availability and representation learning. Recently, self-supervised learning has seen success in pretraining text embeddings and has been applied broadly on related tasks with sparse data, while pretrained audio embeddings based on self-supervised learning are rarely investigated. This paper proposes DEPA, a self-supervised, pretrained depression audio embedding method for depression detection. An encoder-decoder network is used to extract DEPA on in-domain depressed datasets (DAIC and MDD) and out-domain (Switchboard, Alzheimer's) datasets. With DEPA as the audio embedding extracted at response-level, a significant performance gain is achieved on downstream tasks, evaluated on both sparse datasets like DAIC and large major depression disorder dataset (MDD). This paper not only exhibits itself as a novel embedding extracting method capturing response-level representation for depression detection but more significantly, is an exploration of self-supervised learning in a specific task within audio processing.