Existing pre-trained language models (PLMs) have demonstrated the effectiveness of self-supervised learning for a broad range of natural language processing (NLP) tasks. However, most of them are not explicitly aware of domain-specific knowledge, which is essential for downstream tasks in many domains, such as tasks in e-commerce scenarios. In this paper, we propose K-PLUG, a knowledge-injected pre-trained language model based on the encoder-decoder transformer that can be transferred to both natural language understanding and generation tasks. Specifically, we propose five knowledge-aware self-supervised pre-training objectives to formulate the learning of domain-specific knowledge, including e-commerce domain-specific knowledge-bases, aspects of product entities, categories of product entities, and unique selling propositions of product entities. We verify our method in a diverse range of e-commerce scenarios that require domain-specific knowledge, including product knowledge base completion, abstractive product summarization, and multi-turn dialogue. K-PLUG significantly outperforms baselines across the board, which demonstrates that the proposed method effectively learns a diverse set of domain-specific knowledge for both language understanding and generation tasks. Our code is available.