Though Large Language Models (LLMs) have shown remarkable open-generation capabilities across diverse domains, they struggle with knowledge-intensive tasks. To alleviate this issue, knowledge integration methods have been proposed to enhance LLMs with domain-specific knowledge graphs using external modules. However, they suffer from data inefficiency as they require both known and unknown knowledge for fine-tuning. Thus, we study a novel problem of integrating unknown knowledge into LLMs efficiently without unnecessary overlap of known knowledge. Injecting new knowledge poses the risk of forgetting previously acquired knowledge. To tackle this, we propose a novel Infuser-Guided Knowledge Integration (InfuserKI) framework that utilizes transformer internal states to determine whether to enhance the original LLM output with additional information, thereby effectively mitigating knowledge forgetting. Evaluations on the UMLS-2.5k and MetaQA domain knowledge graphs demonstrate that InfuserKI can effectively acquire new knowledge and outperform state-of-the-art baselines by 9% and 6%, respectively, in reducing knowledge forgetting.