Artificial intelligence (AI) is significantly transforming scientific research. Explainable AI methods, such as concept-based models (CMs), are promising for driving new scientific discoveries because they make predictions based on meaningful concepts and offer insights into the prediction process. In molecular science, however, explainable CMs are not as common compared to black-box models like Graph Neural Networks (GNNs), primarily due to their requirement for predefined concepts and manual label for each instance, which demand domain knowledge and can be labor-intensive. This paper introduces a novel framework for Automated Molecular Concept (AutoMolCo) generation and labeling. AutoMolCo leverages the knowledge in Large Language Models (LLMs) to automatically generate predictive molecular concepts and label them for each molecule. Such procedures are repeated through iterative interactions with LLMs to refine concepts, enabling simple linear models on the refined concepts to outperform GNNs and LLM in-context learning on several benchmarks. The whole AutoMolCo framework is automated without any human knowledge inputs in either concept generation, labeling, or refinement, thereby surpassing the limitations of extant CMs while maintaining their explainability and allowing easy intervention. Through systematic experiments on MoleculeNet and High-Throughput Experimentation (HTE) datasets, we demonstrate that the AutoMolCo-induced explainable CMs are beneficial and promising for molecular science research.