Nuclear instance segmentation and classification provide critical quantitative foundations for digital pathology diagnosis. The emergence of the large-scale pretrained foundational model, Segment Anything Model (SAM), has provided a novel solution for nuclear instance segmentation. However, SAM imposes a strong reliance on precise prompts, and its class-agnostic design renders its classification results entirely dependent on the provided prompts. Therefore, we focus on generating prompts with more accurate localization and classification and propose APSeg, Auto-Prompt model with acquired and injected knowledge for nuclear instance Segmentation and classification. APSeg incorporates two knowledge-aware modules: (1) Distribution-Guided Proposal Offset Module (DG-POM), which learns distribution knowledge through density map, and (2) Category Knowledge Semantic Injection Module (CK-SIM), which injects morphological knowledge derived from category descriptions. We conducted extensive experiments on the PanNuke and CoNSeP datasets, demonstrating the effectiveness of our approach. Code is available at https://github.com/hotaru-X/APSeg