As the demand for more personalized recommendation grows and a dramatic boom in commercial scenarios arises, the study on multi-scenario recommendation (MSR) has attracted much attention, which uses the data from all scenarios to simultaneously improve their recommendation performance. However, existing methods tend to integrate insufficient scenario knowledge and neglect learning personalized cross-scenario preferences, thus leading to sub-optimal performance. Meanwhile, though large language model (LLM) has shown great capability of reasoning and capturing semantic information, the high inference latency and high computation cost of tuning hinder its implementation in industrial recommender systems. To fill these gaps, we propose an LLM-enhanced paradigm LLM4MSR in this work. Specifically, we first leverage LLM to uncover multi-level knowledge from the designed scenario- and user-level prompt without fine-tuning the LLM, then adopt hierarchical meta networks to generate multi-level meta layers to explicitly improve the scenario-aware and personalized recommendation capability. Our experiments on KuaiSAR-small, KuaiSAR, and Amazon datasets validate significant advantages of LLM4MSR: (i) the effectiveness and compatibility with different multi-scenario backbone models, (ii) high efficiency and deployability on industrial recommender systems, and (iii) improved interpretability. The implemented code and data is available to ease reproduction.